Inclusion Criteria:

* Physicians should consider whether any of the following may render the patient inappropriate for this protocol:

  * Psychiatric illness which would prevent the patient from giving informed consent
  * Medical conditions such as uncontrolled infection, uncontrolled diabetes mellitus or cardiac disease which, in the opinion of the treating physician, would make this protocol unreasonably hazardous for the patient

    * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
    * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated
    * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load
  * Patients with a "currently active" second malignancy other than non-melanoma skin cancers or cervical carcinoma in situ. Patients are not considered to have a "currently active" malignancy if they have completed therapy and are free of disease for \>= 3 years
* In addition:

  * Women and men of reproductive potential should agree to use an appropriate method of birth control throughout their participation in this study due to the teratogenic potential of the therapy utilized in this trial. Appropriate methods of birth control include abstinence, oral contraceptives, implantable hormonal contraceptives or double barrier method (diaphragm plus condom)

    * A female of childbearing potential is a sexually mature female who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months)
* Histologically or cytologically confirmed malignant peritoneal mesothelioma for which there has been no prior treatment. Given the indolent nature of well-differentiated papillary mesothelioma and multicystic mesothelioma, patients with these variants are not eligible for participation
* Must have measurable disease per RECIST version (v) 1.1
* Not pregnant and not nursing, because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects. Therefore, for women of childbearing potential only, a negative pregnancy test done =\< 28 days prior to registration is required
* Age \>= 18 years
* Eastern Cooperative Oncology Group (ECOG) performance status 0-1
* Leukocytes \>= 2,500/mm\^3
* Absolute neutrophil count (ANC) \>= 1,500/mm\^3
* Platelet count \>= 100,000/mm\^3
* Creatinine clearance \>= 45 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
* Total bilirubin =\< 1.5 x upper limit of normal (ULN)
* Aspartate aminotransferase (AST) / alanine aminotransferase (ALT) =\< 3.0 x upper limit of normal (ULN)
* Urine protein/creatinine (UPC) ratio \< 1, or urine protein: =\< 1+
* No prior systemic therapy for peritoneal mesothelioma is allowed. No concurrent radiotherapy is allowed
* No active or history of autoimmune disease or immune deficiency, including, but not limited to, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, antiphospholipid antibody syndrome, Wegener granulomatosis, Sjogren syndrome, Guillain-Barre syndrome, or multiple sclerosis, with the following exceptions:

  * Patients with a history of autoimmune-related hypothyroidism who are on thyroid-replacement hormone are eligible for the study
  * Patients with controlled Type 1 diabetes mellitus who are on an insulin regimen are eligible for the study
* Patients with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis are excluded) are eligible for the study provided all of following conditions are met:

  * Rash must cover \< 10% of body surface area
  * Disease is well controlled at baseline and requires only low-potency topical corticosteroids
  * No occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high-potency or oral corticosteroids within the previous 12 months
* No history of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, or idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computed tomography (CT) scan
* No prior allogeneic stem cell or solid organ transplantation
* Central nervous system (CNS) metastases must have been treated with local therapy (surgery, radiation, ablation) with systemic steroids tapered to a physiologic dose (10 mg or prednisone equivalent or less)
* Patients who have received live attenuated vaccines within 30 days of the first dose of trial treatment are eligible at the discretion of the investigator. All seasonal influenza vaccines and vaccines intended to prevent SARS-CoV-2 and coronavirus disease 2019 (COVID-19) are allowed
* No history of inadequately controlled hypertension (defined as systolic blood pressure \> 150 mmHg and/or diastolic blood pressure \> 100 mmHg)
* No history of hypertensive crisis or hypertensive encephalopathy
* No clinically significant cardiovascular disease, such as cerebrovascular accidents within 12 months prior to randomization, myocardial infarction within 12 months prior to randomization, unstable angina, New York Heart Association (NYHA) grade II or greater congestive heart failure (CHF), or serious cardiac arrhythmia uncontrolled by medication or potentially interfering with study treatment
* No significant vascular disease (e.g., aortic aneurysm requiring surgical repair or recent arterial thrombosis) within 6 months prior to randomization
* No history of grade \>= 4 venous thromboembolism
* No history or evidence upon physical or neurological examination of central nervous system disease (e.g. seizures) unrelated to cancer unless adequately treated with standard medical therapy
* No history of grade \>= 2 hemoptysis (defined as \>= 2.5 mL of bright red blood per episode) within 1 month prior to screening
* No history or evidence of inherited bleeding diathesis or significant coagulopathy at risk of bleeding (i.e., in the absence of therapeutic anticoagulation)
* No major surgical procedure or significant traumatic injury within 28 days prior to initiation of study treatment (diagnostic laparoscopy is allowed as part of diagnosing peritoneal mesothelioma)
* No core biopsy or other minor surgical procedure, excluding placement of a vascular access device, within 7 days prior to initiation of study treatment
* Placement of a vascular access device should be at least 2 days prior to initiation of study treatment
* No active infection requiring IV antibiotics at the time of initiation of study treatment
* No history of abdominal fistula, gastrointestinal (GI) perforation, intra-abdominal abscess, or active GI bleeding within 6 months prior to randomization
* No serious, non-healing wound, active ulcer, or untreated bone fracture
* No other malignancy within 5 years prior to randomization, except for localized cancer in situ, such as basal or squamous cell skin cancer
* Patients with a creatinine clearance between 45 and 79 mL/min should not use ibuprofen or other nonsteroidal anti-inflammatory drug (NSAIDs) for 2 days before, the day of, and 2 days following pemetrexed administration
* No treatment with immunosuppressive medication (including, but not limited to, corticosteroids, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-TNF-alpha agents) within 2 weeks prior to initiation of study treatment, or anticipation of need for systemic immunosuppressive medication during study treatment, with the following exceptions:

  * Patients who received acute, low-dose systemic immunosuppressant medication or a one-time pulse dose of systemic immunosuppressant medication (e.g., 48 hours of corticosteroids for a contrast allergy) may be eligible for the study
  * Patients who received mineralocorticoids (e.g., fludrocortisone), corticosteroids for chronic obstructive pulmonary disease (COPD) or asthma, or low-dose corticosteroids for orthostatic hypotension or adrenal insufficiency are eligible for the study

* INCLUSION CRITERIA:

Individuals with potentially malignant or suspicious lesions, or with biopsy proven lung cancers or esophageal cancers, malignant pleural mesotheliomas, mediastinal or chest wall neoplasms, thymoma/thymic carcinomas, or thoracic metastases from cancers of non-thoracic origin.

Individuals must have an ECOG performance score of 0-2.

Participants must:

-Have physical examination parameters within acceptable limits by standard of practice guidelines prior to clinically indicated surgical procedure (e.g., biopsy or surgery),

and

-Be aware of the nature of his/her illness,

and

-Must be willing to undergo clinically indicated standard intervention that may include endoscopic biopsies of tumor and adjacent normal tissues (i.e., other tissue necessary to obtain negative margins per standard of care surgical processes) as a part of their standard of care treatment plan.

Participants must agree to provide blood and urine samples to support ongoing laboratory research endeavors pertaining to the epigenetics of thoracic malignancies.

Individuals must be 2 years of age or older. Note: Individuals \>= 2 and \< 18 years of age may only participate in research sample collection if the tissue acquisition is performed during a clinically indicated surgical procedure (e.g., biopsy or surgery), and the biospecimen sampling (e.g., blood, urine, \[clinically indicated\] resected tumor tissue) does not add risk to the clinically indicated procedures.

Ability of participant, their parents/guardians or legally authorized representative (LAR) to understand and the willingness to sign a written informed consent document.

EXCLUSION CRITERIA:

None.

* INCLUSION CRITERIA:
* Confirmation of peritoneal carcinomatosis from peritoneal mesothelioma or atypical mesothelial proliferation, or from appendiceal, colorectal, or ovarian, histologies by the Laboratory of Pathology, NCI.
* Measurable or evaluable disease as defined by RECIST v1.1. criteria and/or by peritoneal carcinomatosis index (PCI) score.
* Participants must be assessed to be able to undergo optimal cytoreduction (i.e., completeness of cytoreduction score of 1 or 0) with laparoscopically assessed PCI score threshold as indicated below:

  * Primary Histology: Appendiceal/Colorectal/Ovarian / PCI Cutoff for Eligibility: Total Score \< 20 (out of 39 possible points)
  * Primary Histology: Mesothelioma or atypical mesothelial proliferation / PCI Cutoff for Eligibility: Total Score \<= 30 (out of 39 possible points)
* Age \>= 18 years.
* ECOG performance status \<= 1 (Karnofsky \>= 80%).
* Participants must have adequate organ and marrow function as defined below:

  * Absolute neutrophil count \>= 1,000/mcL
  * Platelets \>= 75,000/mcL
  * Total bilirubin within \<=1.5x institutional upper limit of normal (ULN)
  * AST (SGOT)/ ALT (SGPT) \<= 3x institutional upper limit of normal (ULN), or \<= 5.0x ULN in participants with liver metastases (only)
  * Creatinine within normal institutional limits

OR

--Creatinine clearance \>= 60 mL/min/1.73 m\^2 for participants with creatinine levels above institutional normal calculated using eGFR.

* Because therapeutic agents used in this trial are known to be teratogenic, individuals of child-bearing potential (IOCBP) and individuals who are able to father a child must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for 180 days after last study treatment.
* Ability of participant to understand and the willingness to sign a written informed consent document.
* Ability and willingness of the participant to co-enroll on the tissue collection protocol 13C0176, Tumor, Normal Tissue and Specimens from Patients Undergoing Evaluation or Surgical Resection of Solid Tumors .

EXCLUSION CRITERIA:

* Participants with known extra-abdominal metastatic disease from the participant s appendiceal, colorectal, ovarian, or peritoneal mesothelioma primary.
* Participants who have received intraperitoneal chemotherapy or other anti-cancer therapy within the last 4 weeks prior to the start of study treatment.
* Participants who have undergone major surgery within the last 12 weeks prior to the start of study treatment.
* History of allergic reactions attributed to platinum-containing compounds.
* History of dihydropyrimidine dehydrogenase deficiency (only participants with appendiceal or colorectal cancer).
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
* Pregnant individuals are excluded from this study because the protocol involves major abdominal surgery and chemotherapeutic agents with the potential for teratogenic or abortifacient effects. Note: Due to an unknown but potential risk for adverse events in nursing infants secondary to treatment of the participant, nursing (including breastfeeding) should be discontinued if the participant is undergoing treatment (i.e., nursing participants must agree to discontinue nursing activities).
* HIV-positive participants with detectable viral load despite antiretroviral therapy are ineligible because of participants increased risk of lethal infections when treated with marrow-suppressive therapy. HIV-positive participants who have undetectable viral load on antiretroviral therapy may be considered for this study only after consultation with a NIAID physician.

* Inclusion Criteria for Genetic Testing:

Cohort 1:

* Participant with pathology confirming a diagnosis of mesothelioma.
* Participant must have a deleterious germline BAP1 mutation. Results from either research or clinical analyses are sufficient for this criterion.

OR

* Participant with mesothelioma otherwise eligible for genetic testing in Cohort 2
* Age \>= 2 years

Cohort 2:

-Individual with a germline BAP1 mutation who does not have a history of mesothelioma (other cancers are allowed). Results from either research or clinical analyses are sufficient for this criterion.

OR

-Individual with no history of mesothelioma with:

--A biological first degree relative (living or deceased) with a history of mesothelioma

OR

--A first degree biological relative with a CLIA (or equivalent) confirmed germline mutation in BAP1

OR

--A second degree biological relative with a CLIA (or equivalent) confirmed germline mutation in BAP1 if relevant first degree relative is deceased or unavailable for testing,

OR

--A second degree biological relative with mesothelioma and a CLIA (or equivalent) confirmed germline mutation in BAP1

-Age \>= 2 years

All participants must understand and be willing to sign a written informed consent

Exclusion Criteria for Genetic Testing

None

Inclusion Criteria for Surveillance:

Inclusion Criteria for Surveillance

* Genetic testing criteria including age restrictions for respective cohorts must be met.
* Participants in Cohort 1 may be enrolled with positive results for germline BAP1 mutation regardless of CLIA (or equivalent) confirmation
* Participants in Cohort 2:

  * must have CLIA (or equivalent) confirmed germline BAP1 mutation

Exclusion Criteria for Surveillance

None

Inclusion Criteria:

* Are ≥ 18 years of age (or the minimum age of consent in accordance with local regulations) at the time of signing the ICF.
* Have a histologically confirmed diagnosis of a locally advanced recurrent or metastatic solid tumor type of interest with MTAP deletion (for dose escalation: mesothelioma \[pleural or peritoneal\], gastroesophageal cancers \[squamous and adenocarcinoma of esophagus, gastric adenocarcinoma, gastroesophageal junction cancers\], pancreatic adenocarcinoma and biliary tract carcinomas (intrahepatic and extrahepatic cholangiocarcinoma, and gallbladder cancer), NSCLC \[adenocarcinoma, squamous cell carcinoma, and adeno-squamous\] or UC \[including mixed urothelial-squamous histology\]; for dose expansion: NSCLC that has progressed on at least one prior line of treatment and for which additional effective standard therapy is not available or for which the participant is not a candidate due to intolerance).
* Are willing and able to provide blood/tumor tissue samples for biomarker testing. An archival tumor tissue specimen must be provided for central confirmation of MTAP loss.
* Must be willing and able to provide the blood/serum/plasma samples
* Have evidence of homozygous loss of MTAP or MTAP deletion (pre-screening available after signing pre-screening ICF)
* Have at least 1 measurable lesion according to RECIST version 1.1
* Have Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) score of 0 or 1
* Have life expectancy \> 3 months
* Have adequate bone marrow and organ function
* Able to swallow and retain orally administered study drug/IMP.
* Are willing and able to comply with all scheduled visits, treatment plan, laboratory tests, lifestyle considerations, and other study procedures
* Male and female: willing to use contraception

Exclusion Criteria:

* Known symptomatic brain metastases requiring supraphysiologic doses of systemic corticosteroids
* Have a known primary central nervous system (CNS) malignancy
* Have had other malignancies within 2 years prior to the first dose, with some exceptions
* Impaired cardiac function or clinically significant cardiac diseases
* Have presence of uncontrolled pleural, peritoneal, or pericardial effusion within 2 weeks before the first study dose, requiring recurrent drainage procedures or an indwelling drainage catheter
* Have a history of severe infections within 4 weeks prior to the start of study treatment
* Hypertension (e.g., \> 150/100 mmHg) that cannot be controlled by medications despite optimal medical therapy
* Other acute or chronic medical or psychiatric condition
* Have a history of immunodeficiency, with a positive human immunodeficiency virus(HIV) test at screening
* Known or suspected viral hepatitis with a positive test at screening
* Had an adverse reaction to a previous antitumor treatment that has not recovered to CTCAE Grade ≤ 1
* Have received chemotherapy within 4 weeks of the first dose of IMP; immunotherapy or biologic targeted antitumor treatments within 2 weeks before the first dose of IMP; small molecule inhibitors within 2 weeks before the first dose of IMP, or other investigational products within 4 weeks
* Current radiation-related toxicity or radiation therapy within 2 weeks before the first dose of IMP
* Administration of any of the following within 2 weeks before the first dose of IDE892 as a monotherapy: Strong inhibitors or inducers of cytochrome P450, Strong inhibitors of P-glycoprotein, Narrow therapeutic index and sensitive substrates of multidrug and toxin extrusion (MATE)1 and MATE2-K, Narrow therapeutic index and sensitive substrates of P-gp and breast cancer resistance protein
* Administration of any of the following within 2 weeks before the first dose of IDE892: Strong inhibitors or inducers of CYP3A4/5, Strong inhibitors of P-gp and/or BCRP, Narrow therapeutic index and sensitive substrates of MATE1 and MATE2-K, Narrow therapeutic index and sensitive substrates of P-gp and BCRP
* Use of proton pump inhibitors (PPIs) within 7 days prior to the first dose of IMP or planned use during the study
* Use of drugs with known risk for QT prolongation within 2 weeks prior to the first dose of IDE892
* Previous treatment with a Amethionine adenosyltransferase 2A (MAT2A) inhibitor and/or Protein arginine N-methyltransferase (PRMT) inhibitor
* Major surgery within 4 weeks before study entry
* Prior irradiation to \> 25% of the bone marrow
* Known or suspected hypersensitivity to IDE892

Disease-Specific Eligibility Criteria Eligibility Criteria for Participants with NSCLC (All Parts)

* Must have histologically confirmed diagnosis of advanced or metastatic NSCLC that has progressed after prior treatment with platinum chemotherapy and a PD-1/PD-L1 inhibitor (unless contraindicated or participant developed intolerance) in the metastatic setting
* Treatment with no more than 3 prior lines in the setting of advanced or metastatic disease.
* If considered standard of care and available, participants whose cancers have proven targetable oncogene alterations must have had disease progression on (unless contraindicated or participant developed intolerance) at least 1 prior line containing appropriate targeted therapy.

Eligibility Criteria for Participants with Urothelial Cancer (Bladder and Upper Urinary Tract), Mesothelioma (Pleural or Peritoneal), Pancreatic Adenocarcinoma or Biliary Tract Carcinomas (Intrahepatic and Extrahepatic Cholangiocarcinoma, and Gallbladder Cancer) (Parts 1 and 3)

* Must have histologically confirmed diagnosis of advanced or metastatic UC, mesothelioma, gastroesophageal cancer or pancreatic and biliary tract tumors
* Must have progressed following at least 1 prior line of therapy
* Treatment with no more than 3 prior lines in the setting of advanced or metastatic disease

Inclusion Criteria:

* Patient age 18 years or older, both sexes.
* Clinical diagnosis of MPM at enrolling institution.
* Prior to randomization, intraoperative pathologic confirmation of epithelioid MPM at enrolling institution.
* Complete or near-complete CRS achieved.
* Patient must be planning to undergo complete cytoreduction of all peritoneal disease.
* ECOG performance status ≤ 1.
* Hematology: ANC ≥ 1,500/µl.
* Platelets \> 75,000/µl.
* Adequate renal function: creatinine \< 1.5× the upper limit of normal (ULN) or calculated creatinine clearance of ≥50 ml/min.
* Adequate hepatic function: bilirubin \< 1.5 mg/dl (except in patients with Gilbert's syndrome, who must have total bilirubin \< 3.0 mg/dL).
* Women of childbearing potential with a negative pregnancy test result (urine or blood) who agree to use an effective contraceptive method. Reliable contraception should be used from trial screening and must be continued throughout the study. A woman of childbearing potential is defined as one who is biologically capable of becoming pregnant.
* A man participating in this study must agree to utilize a reliable barrier form of contraception for the duration of the study
* Signed and dated written informed consent to participate in this clinical trial must be obtained prior to any study procedure.

Exclusion Criteria:

* Subjects who have previously undergone intraperitoneal chemotherapy or systemic chemotherapy for peritoneal mesothelioma.
* Subjects who have previously received platinum-containing chemotherapy regimens.
* Subjects with preoperative or intraoperative biopsy consistent with sarcomatoid mesothelioma, well-differentiated papillary mesothelioma, or benign multicystic mesothelioma.
* Other prior malignancies, except for cured non-melanoma skin cancer, curatively treated in situ carcinoma of the cervix, adequately treated malignancies for which there has been no evidence of activity for more than three years, or indolent tumors for which observation over two years is a reasonable option.
* High suspicion for extra-abdominal metastases.
* Women who are pregnant or lactating.
* Active coronary artery disease (defined as unstable angina or a positive cardiac stress test). Subjects with a history of coronary artery disease may be included if they have had a normal stress test within 60 days of enrollment or are determined by a cardiologist to be of acceptable perioperative risk.
* Uncontrolled hypertension defined as \>140/90 and not cleared for surgery at the time of consent.
* New York Heart Association (NYHA) Class II or higher congestive heart failure; restrictive or obstructive pulmonary disease that would limit study compliance or place the patient at unacceptable risk for participation in the study.
* History of cerebrovascular disease that would limit study compliance or place the patient at unacceptable risk for participation in the study.
* Subjects with other concurrent severe medical problems unrelated to the malignancy that would significantly limit full compliance with the study or place them at an unacceptable risk for participation in the study.
* Patients with known cisplatin, carboplatin, pemetrexed or mitomycin allergy.
* Evidence of extensive intraperitoneal adhesions at the time of surgery which prohibits intraperitoneal therapy, as determined by the operating surgeon.
* Any condition that would preclude the ability to deliver appropriate IP therapy.
* Use of an oral medication, lacking a suitable non-oral substitute, that if held for up to ten days, would be felt an unacceptable risk by the investigator.
* Life expectancy \< 12 weeks.

Key Inclusion Criteria:

All Patients:

* Adults aged ≥18 years with life expectancy ≥12 weeks
* ECOG performance status 0-1
* Adequate recovery from prior therapy-related toxicities (Grade ≤1, with exceptions)
* Adequate bone marrow, renal, and hepatic function per protocol-defined thresholds
* Willingness to provide tumor tissue and blood samples for biomarker analyses
* Agreement to protocol-specified contraception requirements
* Signed informed consent prior to study procedures

Disease-Specific Inclusion Criteria:

Phase 1 (Dose Escalation):

* Histologically or cytologically confirmed locally advanced or metastatic solid tumors or lymphoma
* Disease refractory to standard therapy or with no available effective standard treatment
* For prostate cancer: castrate testosterone levels maintained throughout the study

Phase 2 (Disease-Specific Cohorts):

* M1: ARID1A mutant urothelial carcinoma or other ARID1A mutant solid tumors (with cohort specific prior therapy and RECIST 1.1 measurable disease requirements)
* M2: ARID1A mutant ovarian clear cell carcinoma after prior platinum-based therapy (and bevacizumab unless contraindicated)
* M3: ARID1A mutant recurrent/metastatic endometrial carcinoma after platinum therapy and appropriate immunotherapy
* M4: Relapsed/refractory peripheral T cell lymphoma or diffuse large B cell lymphoma, transplant-ineligible, with measurable disease
* M5: Relapsed/refractory pleural or peritoneal mesothelioma with documented BAP1 loss
* M6: Metastatic castration-resistant prostate cancer (mCRPC) with documented progression after AR targeted therapy and taxane chemotherapy
* M7: ARID1A wild type endometrial carcinoma (exploratory food-effect cohort)
* M8: mCRPC treated with DZR123 in combination with enzalutamide, with cohort specific requirements for prior androgen receptor pathway inhibitor and chemotherapy exposure

Key Exclusion Criteria:

All Patients:

Medical Conditions:

* Prior solid organ or allogeneic hematopoietic cell transplant
* Active or untreated symptomatic CNS metastases (with limited exceptions)
* Clinically significant cardiovascular disease, including uncontrolled arrhythmias or prolonged QTc
* Active interstitial lung disease or pneumonitis
* Uncontrolled infections or significant gastrointestinal disorders affecting absorption
* Active HIV or hepatitis B/C infection
* Concurrent malignancy requiring active treatment (with protocol-defined exceptions)
* Pregnancy, breastfeeding, or inability to comply with protocol requirements

Prior or Concomitant Therapy:

* Recent anticancer therapy within protocol-defined washout periods
* Prior EZH2 inhibitor treatment
* Recent radiation or liver-directed therapies outside allowed windows
* Use of strong CYP3A4/5 inhibitors or inducers

Additional Cohort-Specific Exclusions:

* M6 (mCRPC): Bone-only disease, unstable bone lesions, PSA-lowering herbal products, recent prohibited prostate cancer therapies
* M8 (Combination): PSA-only disease, prior investigational androgen receptor pathway inhibitors, significant seizure risk, extensive prior bone marrow irradiation, active inflammatory gastrointestinal disease

Key Inclusion Criteria:

* Histologically confirmed, metastatic, or unresectable solid cancer that has either not responded to or progressed during or after appropriate prior systemic anticancer therapy including chemotherapy, immunotherapy, radiation therapy, or appropriate targeted therapy, or for which there is no treatment available or prior SOC therapy was not tolerated and for which there is no further SOC treatment available
* Part 1: must have one of the following:

  * Mesothelioma with or without NF2 mutations
  * Advanced solid tumors with NF2 mutations
  * Advanced solid tumors with other Hippo pathway mutations or fusions (e.g., FAT1, LATS1/2, YAP fusions; WWTR1-CAMTA1 in EHE).
* Part 2: must have the tumor histology and oncogenic mutation or genomic aberration specific to each dose expansion cohort defined below:

  * Cohort 1: Participants with mesothelioma with or without NF2 mutations
  * Cohort 2: Participants with advanced solid tumors with NF2 mutations
  * Cohort 3: Participants with advanced solid tumors with other Hippo pathway mutations identified during Part 1 (Phase 1a) dose escalation
  * Cohort 4: SW-682 with appropriate combination therapy.
* In both parts, participants should have known oncogenic mutation identified by Next Generation Sequencing or local assay
* Must have archival tumor tissue or agree to a fresh tumor biopsy at screening
* Measurable disease per RECIST 1.1
* Eastern Cooperative Oncology Group (ECOG) performance status of ≤1
* Adequate bone marrow, kidney, hepatic, and coagulation function

Key Exclusion Criteria:

* Evidence of symptomatic CNS metastases, leptomeningeal carcinomatosis, or untreated spinal cord compression
* Clinically significant cardiac disease or abnormal cardiac parameters
* Preexistence or inheritance of a familial renal syndrome
* Concomitant non-anti-arrhythmic medications that are known to prolong the QTc interval
* Concomitant medicines that are known strong/moderate inhibitors or inducers of cytochrome P450 3A4 (CYP3A4) and/or CYP1A2 within 14 days or 5 half-lives before the first dose of study treatment
* Concomitant medicines that are known sensitive substrates of CYP3A4, CYP2C19, CYP2D6, CYP1A2, and/or CYP2B6 within 14 days or 5 half-lives before the first dose of study treatment
* Concomitant medicines that are known sensitive substrates of PGP, BCRP, OATP1B1, OATP1B3, OAT1, OAT3, MATE1, MATE2-K, OCT2
* Clinically significant active infection (bacterial, fungal, or viral)

Inclusion Criteria:

* Male or female ≥18 years of age.
* Life expectancy \>3 months.
* ECOG performance status 0-1.
* Histologically/cytologically confirmed advanced or metastatic solid tumors that have progressed on or are intolerant/unsuitable for standard therapies. Eligible tumor types: TNBC, HR+ breast cancer, colon cancer, gastric cancer, HCC, NSCLC (adeno and squamous), mesothelioma, pancreatic cancer, HRPC, soft tissue sarcoma; other tumor types after Medical Monitor discussion. Stable CNS metastases ≥4 weeks post-radiotherapy and off steroids ≥14 days are permitted.
* ≥1 measurable lesion per RECIST v1.1 (prostate cancer with bone-only disease and elevated PSA assessed by PCWG3).
* Accessible tumor for biopsy
* Adequate organ/bone marrow function.
* Willingness and ability to provide informed consent.
* Negative serum pregnancy test and use of effective contraception through 90 days after last dose for women of childbearing potential.
* Male participants must use barrier contraception or abstinence and not donate sperm through 90 days after last dose.

Exclusion Criteria:

* High-risk cardiovascular disease.
* Concurrent anti-cancer treatment.
* Active infection requiring systemic treatment within 2 weeks pre-dose.
* History of another malignancy (with standard exceptions for in situ disease, non-melanoma skin cancers, and remission ≥2 years).
* Active HBV (HBV-DNA \>ULN), HCV (HCV-RNA \>ULN), or HIV (well-controlled HIV with CD4 ≥350 cells/µL and undetectable viral load permitted); AIDS-defining opportunistic infection within 12 months.
* Compromised pulmonary function within 6 months pre-dose .
* Pregnancy or breastfeeding.
* Recent radiotherapy, systemic anti-tumor therapy, other investigational therapy without appropriate washout.
* Major surgery ≤4 weeks pre-dose.
* Unable to swallow tablets or conditions affecting GI absorption.
* Any medical or psychiatric disorders affecting compliance and/or interpretation of study results.
* Persistent toxicities from prior anti-cancer therapy (exceptions apply)
* Clinically significant corneal disease.
* Unable to comply with prohibited concomitant medication restrictions.

* INCLUSION CRITERIA:
* All participants \>= 2 years of age with malignant mesothelioma.
* All participants \>=18 years of age with thymic carcinoma, pancreatic or biliary adenocarcinoma or lung, gastric or ovarian cancers or other solid tumor known to express mesothelin.
* Confirmed pathological diagnosis is required
* Ability and willingness of participant to provide informed consent to participation.

EXCLUSION CRITERIA:

* Active symptomatic major organ disorder that would increase the risk of biopsy, including but not limited to ischemic heart disease, recent myocardial infarction, active congestive heart failure, pulmonary dysfunction.
* Pregnant women.
* Active concomitant medical or psychological illnesses that may increase the risk to the participant or in adult participants, inability to obtain informed consent, at the discretion of the principal investigator.

Part A

Inclusion Criteria:

1. Provide written informed consent.
2. 18 years old or older.
3. Advanced, metastatic, and/or progressive solid tumors for whom there is no authorized or effective therapy available, or for whom such therapies are considered inappropriate by the Investigator.
4. Measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) Version 1.1.
5. Eastern Cooperative Oncology Group (ECOG) performance status of 0-1.

Exclusion Criteria:

1. Subjects with known human epidermal growth factor receptor 2 (HER2+) overexpressing malignancies.
2. Radiotherapy (except for palliative reasons), endocrine therapy, chemotherapy, or investigational agent within 28 days, (42 days for nitrosoureas, mitomycin-C) of first dose of NXP900. Subjects can continue to receive bisphosphonates due to metastatic bone disease or GnRH agonists if they have prostate cancer.
3. Ongoing toxic manifestations of previous treatments \> Grade 2 with the exception of alopecia and neuropathy.
4. Subjects with treated brain metastases with evidence of progression within 28 days after central nervous system (CNS)-directed treatment, as ascertained by clinical examination and brain imaging (magnetic resonance imaging \[MRI\] or computed tomography \[CT\] scan) during the Screening period.
5. Female subjects who can become pregnant (or are already pregnant or lactating), unless they have a negative serum pregnancy test before enrollment and agree to use at least one highly effective form of contraception .
6. Male subjects with partners of childbearing potential, unless they agree to take measures not to father children by using a barrier method of contraception (condom plus spermicide).
7. Major surgery from which the subject has not yet recovered.

Part B:

Inclusion Criteria:

1. Provide written informed consent.
2. 18 years old or older.
3. Advanced, metastatic, and/or progressive solid tumors with pathogenic molecular alterations:

   1. Non-small cell lung cancer (adenocarcinoma); YES1, TYMS amplification or FAT1 pathogenic mutation
   2. Non-small cell lung cancer (squamous cell carcinoma); YES1, TYMS amplification or FAT1 pathogenic mutation
   3. Renal cancer; NF2 pathogenic mutation
   4. Mesothelioma; NF2 pathogenic mutation
   5. Other solid tumors with a NF2, FAT1 or LATS1 pathogenic gene mutation or TYMS, YAP1, YES1, or TAZ1 gene amplification, or cholangiocarcinoma with IDH1 or IDH2 mutations.
4. Must have received 1-3 prior therapies appropriate for their tumor type and stage of disease
5. Measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) Version 1.1 (or mRECIST 1.1 for subjects with pleural mesothelioma).
6. Eastern Cooperative Oncology Group (ECOG) performance status of 0-1.

Exclusion Criteria:

1. Subjects with the following combination of cancer type and pathogenic molecular alterations are excluded:

   1. Subjects with colorectal cancer, glioma, melanoma, or anaplastic thyroid conditions with BRAF mutations.
   2. Subjects with NSCLC with BRAF or EGFR mutations or HER2 overexpression.
   3. Subjects with breast cancer, gastric cancer, esophageal junction adenocarcinoma or biliary cancer with HER2 alterations,
2. Subjects with anal, penile, cervical or head and neck cancers with a prior history of human papilloma virus (HPV) infection.
3. Radiotherapy (except for palliative reasons), endocrine therapy, chemotherapy, or investigational agent within 28 days (42 days for nitrosoureas, mitomycin-C) prior to first dose of NXP900. Subjects can continue to receive bisphosphonates due to metastatic bone disease or GnRH agonists if they have prostate cancer.
4. Ongoing toxic manifestations of previous treatments \> Grade 2 with the exception of alopecia and neuropathy.
5. Female subjects who can become pregnant (or are already pregnant or lactating), unless they have a negative serum pregnancy test before enrollment and agree to use at least one highly effective form of contraception .
6. Male subjects with partners of childbearing potential, unless they agree to take measures not to father children by using a barrier method of contraception (condom plus spermicide).
7. Major surgery from which the subject has not yet recovered.

Inclusion Criteria:

Part A and B:

* Histologically or cytologically confirmed metastatic or unresectable solid malignancy including ovarian cancer (must have epithelial ovarian cancer, primary peritoneal cancer, or fallopian tube cancer), endometrial cancer, non-small cell lung cancer (Part A), EGFR-mutated NSCLC (Part B), breast cancer (hormone receptor positive, HER2-negative and triple-negative) (Part A), mesothelioma or cervical cancer (Part B).
* Previously received therapies known to confer clinical benefit.
* Measurable disease per RECIST v1.1 for all tumor types other than pleural mesothelioma which will use mRECIST v1.1 at baseline.

Part C, E, and H:

Participants must have histologically or cytologically confirmed metastatic or unresectable epithelial ovarian cancer as specified below.

* High grade serous ovarian cancer, primary peritoneal cancer, or fallopian tube cancer (excluding endometrioid, clear cell carcinomas, mucinous, low grade, and those with a sarcomatous or neuroendocrine element)
* Participants must have received up to 3 prior lines of therapy. Participants may have had up to to 4 prior lines of therapy are allowed if MIRV is locally approved and was used as the last line of therapy. Participants must have progressed radiographically on or after their most recent line of therapy.
* Participants must have platinum-resistant ovarian cancer.
* Participants must have received prior bevacizumab or approved biosimilar.
* Participants with known or suspected deleterious germline or somatic BRCA mutations (as determined by Food and Drug Administration \[FDA\]-approved test in a Clinical Laboratory Improvement Amendments \[CLIA\]-certified laboratory; or locally approved equivalent) and who achieved a complete or partial response to platinum-based chemotherapy must have been treated with a poly ADP-ribose polymerase (PARP) inhibitor as maintenance treatment.
* Measurable disease per the RECIST v1.1 at baseline.

Part D:

Cohort D1:

* Participants must have platinum-sensitive ovarian cancer.
* Participants must have received 1 to 3 prior lines of therapy.

Cohort D2:

* Participants must have primary platinum-refractory, platinum-resistant, or platinum-sensitive ovarian cancer.
* Participants with primary platinum-refractory ovarian cancer must have received ≤2 prior lines of therapy. Primary platinum-refractory ovarian cancer is defined as a lack of response or by progression within 91 days after completing front-line platinum containing therapy.
* Participants must have received 1 to 3 prior lines of therapy for platinum-resistant ovarian cancer (PROC), and up to 4 prior lines of therapy for platinum-sensitive ovarian cancer (PSOC). Prior treatments may have included bevacizumab, PARP inhibitor, and MIRV.

  * Participants with PSOC must have disease progression on or after maintenance treatment, or at least 6 months (\>183 days) or more from the last dose of platinum-based therapy.

Cohort D3:

• Endometrial cancer (any subtype excluding sarcoma).

Cohort D4:

• Primary advanced or recurrent endometrial cancer (any subtype excluding sarcoma and neuroendocrine tumors).

Part F and G:

* Participants must have histologically or cytologically confirmed EC.
* Recurrent progressive EC (any subtype excluding neuroendocrine tumors, carcinosarcoma, or endometrial sarcoma) following prior therapy.
* Participants must have received 1 to 3 prior lines of therapy, and must have progressed radiographically on or after their most recent line of therapy:
* Participants must have received prior platinum-based chemotherapy and a programmed death-ligand 1 (PD-\[L\])1 inhibitor.
* Participants who progress \>12 months after completion of prior adjuvant or neoadjuvant platinum-based chemotherapy must receive 1 additional cytotoxic systemic treatment prior to enrollment in this study.
* Hormonal therapy alone (i.e., without chemotherapy) will not be counted as a separate line of therapy.
* Measurable disease per the RECIST Version 1.1 at baseline.

Part I:

* Participants must have histologically or cytologically confirmed high grade serous or endometrioid epithelial ovarian cancer, fallopian tube cancer and primary peritoneal cancer (excluding clear cell, mucinous, or sarcomatous histology, mixed tumors containing any of the above histologies or low grade/borderline ovarian tumors).
* Participants must have platinum sensitive ovarian cancer.
* Measurable disease per the RECIST Version 1.1 at baseline.

Part J:

* Participants must have high grade epithelial ovarian cancer, primary peritoneal cancer, or fallopian tube cancer including serous, endometrioid, and clear cell carcinomas, and excluding mucinous, low grade, and those with a sarcomatous or neuroendocrine element.
* Measurable disease per the RECIST Version 1.1 at baseline.

Part K:

* Participants must have histologically or cytologically confirmed metastatic or unresectable ovarian cancer (must have high grade epithelial ovarian cancer, primary peritoneal cancer, or fallopian tube cancer including serous, endometrioid, and clear cell carcinomas, and excluding mucinous, low grade, and those with a sarcomatous or neuroendocrine element).
* Participants must have primary platinum-refractory, platinum-resistant, or platinum-sensitive ovarian cancer.
* Measurable disease per the RECIST Version 1.1 at baseline.

Exclusion Criteria:

* History of (non-infectious) interstitial lung disease (ILD)/pneumonitis that required steroids within the past 2 years, has current ILD/pneumonitis, or where suspected ILD/pneumonitis cannot be ruled out by imaging at screening.
* Prior therapy with a topoisomerase 1 inhibitor-based antibody drug conjugate.

Note: Other protocol-defined inclusion/exclusion may apply.

Inclusion Criteria:

* Age ≥18 at the time of signing the ICF.
* Provision of tumor sample to assess the PD-L1 expression (if applicable).
* ECOG performance status of 0 or 1.
* Measurable disease according to RECIST 1.1 (variations of RECIST 1.1 if applicable).
* Life expectancy ≥ 12 weeks.
* Adequate organ and bone marrow function.
* Body weight \> 35 kg
* Capable of giving signed informed consent.

Exclusion Criteria:

* Spinal cord compression.
* For sub-study 1,2,3,4, brain metastases unless asymptomatic, stable, and not requiring steroids for at least 14 days prior to start of study intervention. For sub-study 5, participants with untreated or progressive brain metastases.
* For sub-study 1,2,3, participants with primary neuroendocrine, mesenchymal, sarcomatoid histologies, or other histologies not mentioned as part of the inclusion criteria.
* Have not recovered (ie, ≤ Grade 1 or at baseline) from an AE due to a previously administered anti-cancer therapy.
* For sub-study 2, have had radiotherapy within 2 weeks prior to enrollment.
* For sub-study 3,4, participants have contraindications to any of the following drugs: 5-FU, paclitaxel and carboplatin
* History of another primary malignancy except for a) Malignancy treated with curative intent with no known active disease ≥2 years before the first dose of study intervention and of low potential risk for recurrence; b) Adequately treated nonmelanoma skin cancer or lentigo maligna, or carcinoma in situ without evidence of disease.
* Any evidence of diseases, and/or history of organ transplant or allogenic stem cell transplant, which makes it undesirable for the participant to participate in the study or that would jeopardize compliance with the protocol.
* Evidence of the following infections: active infection including tuberculosis; known HIV infection. that is not well controlled; active or uncontrolled HBV or HCV; or active hepatitis A.
* History of active primary immunodeficiency or active or prior documented autoimmune or inflammatory disorders.
* Participants who are candidates for curative therapy.
* Prior exposure to any immune-mediated therapy.
* Current or prior use of immunosuppressive medication within 14 days before the first dose of the study intervention is excluded. The following are exceptions to this criterion: a) Intranasal, inhaled, topical steroids, or local steroid injections (eg, intraarticular injection); b) Steroids as premedication for hypersensitivity reactions (eg, CT scan premedication or chemotherapy premedication) or a single dose for palliative purpose (eg, pain control).
* For sub-study 1,2,3,4, participants are ineligible if they have received any anti-cancer therapy within 28 days prior to the first dose of study intervention or within 5 half-lives of the respective agent, whichever is longer.
* Any concurrent chemotherapy except study intervention, radiotherapy, investigational, biologic, or hormonal therapy for cancer treatment.
* Radiotherapy treatment with a wide field of radiation or to more than 30% of the bone marrow within 4 weeks, prior to the first dose of study intervention.
* Major surgical procedures within 4 weeks prior to the first dose of the study intervention or still recovering from prior surgery.
* Receipt of live attenuated vaccine within 30 days prior to the first dose of the study intervention.
* Participants with a known allergy or hypersensitivity to any study intervention, on any excipients of any study intervention.
* For substudy 5: Participants with any prior systemic therapy, non-palliative radiotherapy, radical pleuropneumonectomy for pleural mesothelioma.

Inclusion Criteria:

* Aged ≥ 18 years
* Satisfactory organ function as determined by laboratory testing
* Eastern Cooperative Oncology Group performance (ECOG) status of 0 to 1
* Life expectancy \> 3 months
* Progressive disease despite standard therapy or for whom no standard therapy exists
* Positive \[203Pb\]Pb-PSV359 SPECT/CT scan showing uptake of \[203Pb\]Pb-PSV359 in at least 1 known lesion on the 1-hour SPECT/ CT scan
* Histological, pathological, and/or cytological confirmation of solid tumor malignancy that is locally advanced or metastatic

Exclusion Criteria:

* Known hypersensitivity to the active agent or any of the excipients
* Active secondary malignancy
* Pregnancy or breastfeeding a child
* Known brain metastases
* Known active or uncontrolled infections requiring ongoing antifungals or antibiotics in the 3 days prior to enrollment
* Known medical condition which would make this protocol unreasonably hazardous for the patient
* Existence of any medical or social issues likely to interfere with study conductor that may cause increased risk to the subject or to others, e.g., lack of ability to follow radiation safety precautions
* Medical history of a condition resulting in a severe allergic reaction such as anaphylaxis or angioedema to known components of the investigational product or excipients
* Major surgery within 21 days prior to the administration of \[212Pb\]Pb-PSV359; the subject must be sufficiently recovered and stable before treatment administration
* Diagnosis of deep vein thrombosis or pulmonary embolism within 4 weeks prior to enrollment into the study
* Current abuse of alcohol or illicit drugs
* Treatment with any live/attenuated vaccine in the 7 days prior to enrollment
* Previous treatment with any systemic anticancer therapy within 4 weeks prior to treatment on study

Inclusion Criteria:

* Sarcomatoid or sarcomatoid-dominant (\> 50%) biphasic, pleural mesothelioma
* Stage: I-IIIA disease per Union for International Cancer Control (UICC) TNM Classification of Malignant Tumours 8th edition
* Measurable disease or non-measurable disease as defined
* No prior treatment which would be considered treatment for the primary neoplasm or impact the primary endpoint
* No treatment with hormones or other chemotherapeutic agents except for hormones administered for non-disease-related conditions (e.g., insulin for diabetes and or hormonal therapy for breast, prostate cancer etc.)
* Not pregnant and not nursing, because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown

  \* Therefore, for women of childbearing potential only, a negative pregnancy test done =\< 14 days prior to registration is required
* Age \>= 18 years
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 or Karnofsky \>= 60%
* Absolute neutrophil count (ANC) \>= 1,000/mm\^3
* Leukocytes \>= 2,000/mm\^3
* Platelet count \>= 100,000/mm\^3
* Creatinine =\< 1.5 x upper limit of normal (ULN) OR creatinine clearance \>= 40 mL/min
* Total bilirubin =\<1.5 x ULN, except patients with Gilbert Syndrome who can have total bilirubin \< 3.0 mg/dl
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3.0 x ULN
* Alkaline (alk) phosphatase (phos) =\< 3.0 x ULN
* No active, known or suspected autoimmune disease except for vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger
* No active systemic infection requiring therapy, as well as positive tests for hepatitis B surface antigen or hepatitis C antibody
* No history of any other condition that may require the initiation of anti-tumor necrosis factor alpha (TNFalpha) therapies or other immunosuppressant medications during the study
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
* Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better
* Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial
* STEP 2 ELIGIBILITY CRITERIA: Completion of at least 1 cycle of treatment and not have an unresolved adverse event that would preclude surgery
* STEP 2 ELIGIBILITY CRITERIA: No evidence of progression that would preclude resection
* STEP 2 ELIGIBILITY CRITERIA: ECOG performance status =\< 2 or Karnofsky \>= 60%
* STEP 2 ELIGIBILITY CRITERIA: Predicted forced expiratory volume in 1 second (FEV1) \> 35% and postoperative predicted diffusion capacity of the lung for carbon monoxide (DLCO) \> 35%
* STEP 2 ELIGIBILITY CRITERIA: Registration to step 2 no less than 21 days and no more than 90 days after the last dose of neoadjuvant therapy

Exclusion Criteria:

* No patients deemed to be unresectable or poor surgical candidates
* No patients with chest wall invasion, peritoneal spread, contralateral pleural involvement, mediastinal organ involvement, vertebral involvement, or metastases to contralateral intrathoracic lymph nodes, or any supraclavicular nodes
* No patients with a history of symptomatic interstitial lung disease

* ELIGIBILITY CRITERIA:

Inclusion Criteria for Genetic Testing

-Eligible participants include:

--Individuals with a history of any malignancy with known or suspected germline mutations involving BAP1

OR

--First- or second-degree relatives of patients (with or without cancer) with documented BAP1 tumor predisposition syndrome (TPDS)

* Age \>= 30 years.
* All participants must understand and be willing to sign a written informed consent document.

Inclusion Criteria for Surveillance

* Eligible participants include those who completed step 1 genetic testing with study-confirmed BAP1 or other germline TPDS mutation.
* Completed co-enrollment on protocol 06C0014, "Prospective Evaluation of Genetic and Epigenetic Alterations in Patients with Thoracic Malignancies."

Inclusion Criteria

* Diagnosis/history of cancer
* Risk for developing cancer or suspicious clinical findings
* No history of cancer (normal control registry)
* Able to provide informed consent
* 19 years of age or older
* English or Spanish speaking individuals

Exclusion Criteria

* Unable to provide informed consent because of cognitive impairment
* Non-English or non-Spanish speaking individuals

Inclusion Criteria:

* Documentation of Disease:
* Patients must have pathologic confirmation of one of three diseases:
* Diffuse pleural mesothelioma (DPM)
* Gastroesophageal carcinoma (GEC) including adenocarcinoma or squamous cell carcinoma of the esophagus, gastroesophageal junction, or stomach.
* PD-L1 CPS ≥1 (using clone 73-10, DAKO)
* HER2 overexpression negative (using clone 4B5, Ventana): HER2 IHC 0-1+, or HER2 2+ with ISH showing HER2:CEP17 ratio \<2 and average HER2 copy number \<6.0 signals/cell
* Urothelial carcinoma (UC)
* Archival tissue is acceptable
* Metastatic or advanced/unresectable disease:
* For Diffuse Pleural Mesothelioma (DPM) and Gastroesophageal Carcinoma (GEC )cohorts: no prior systemic treatment for metastatic disease
* Patients with metastatic disease after treatment for localized GEC may have received prior systemic therapy (chemotherapy and/or chemoradiation) if \>6 months have elapsed between the end of therapy and registration.
* One prior cycle of standard-of-care therapy alone without BMS-986504 or other MTAP inhibitors (ipi/nivo for DPM, FOLFOX + nivo for GEC) is acceptable with PI approval.
* For UC cohort: must have received at least 1 prior line of treatment without prior gemcitabine (prior tx with Gem+Platinum in the perioperative setting is permitted if at least 12 months have elapsed from trial enrollment)
* Patients with recurrent disease within 1 year of completion of prior perioperative systemic therapy are eligible with PI approval.
* One prior cycle of standard-of-care therapy alone with gemcitabine + platinum, without BMS-986504 or other MTAP inhibitors, is acceptable with PI approval.
* Confirmation of MTAP deletion by either IHC or NGS:
* MTAP deletion must be detected by either IHC and/or NGS (including FACETS), done on tumor tissue (not blood):
* IHC (using antibody 1813, NBP2-75730, Novus Biologicals)30
* IHC staining showing loss of MTAP expression
* Tissue-based NGS options
* MSK-IMPACT version 7 or beyond showing homozygous MTAP copy number loss
* FACETS showing homozygous deletion
* Other CLIA-approved commercial Template Version: 1-21-25
* Full report must be available for review and confirmation
* Cases with discordant results between NGS and IHC, in which one test shows MTAP loss/MTAP del and the other shows MTAP intact, are acceptable with PI approval
* Measurable disease per RECIST v 1.1 (or, for DPM cohort, by either RECIST v 1.1 or modified RECIST \[mRECIST\] for mesothelioma31)
* No contraindications to receiving other standard-of-care agents per package inserts (and see Appendix IV), and per the discretion of the PI:
* DPM: Ipilimumab + nivolumab
* GEC: FOLFOX (5-FU, leucovorin, and oxaliplatin) + nivolumab
* UC: Gemcitabine + platinum (carboplatin or cisplatin)
* Age ≥ 18
* KPS ≥ 70/ECOG \<1
* Reproductive Status:
* Female participants of child-bearing potential (as assigned at birth) must have a negative highly sensitive urine or serum (as required by local regulations) pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin) within 24 hours prior to the start of study intervention.
* If a urine test cannot be confirmed as negative (eg, an ambiguous result), a serum pregnancy test is required. In such cases, the participant must be excluded from participation if the serum pregnancy result is positive.
* Female participants of child-bearing potential (as assigned at birth) must agree to use a combination of a hormonal and a non-hormonal contraceptive method or a non-hormonal method alone that is highly effective (with a failure rate of \< 1% per year)during the intervention period and for 14 months (for females) after the last dose of study intervention (or longer if required by institutional guidelines) Hormonal contraceptive methods alone are not allowed.
* Female participants of child-bearing potential (as assigned at birth) must also agree not to donate eggs (ova, oocytes) for the purpose of reproduction for the same period.
* If needed, these participants should be advised to seek advice about egg donation and cryopreservation of germ cells before treatment.
* Female participants (as assigned at birth) are deemed to be without child-bearing potential if they meet one of the following criteria:
* Postmenopausal for at least 1 year before the screening visit
* Permanently sterile (undergone a hysterectomy, bilateral salpingectomy or bilateral oophorectomy) with surgery at least 1 month before the first dose of study drug or confirmed by follicle stimulating hormone (FSH) test \> 40 mIU/mL and estradiol \< 40 pg/mL (\<140 pmol/L)
* Male participants (as assigned at birth) will be required to always use a latex or other synthetic condom during any sexual activity (eg, vaginal, anal, oral) with a female of childbearing potential, even if the participant has undergone a successful vasectomy or if the partner is pregnant or breastfeeding. Male participants (as assigned at birth) should continue to use a condom during the intervention period and for at least 11 months after the last dose of study intervention (or longer if required by institutional guidelines).
* Male participants must refrain from donating sperm during the intervention period and for at least 11 months after the last dose of study intervention (or longer if required by institutional guidelines).
* If needed, male participants should be advised to seek advice about sperm donation and cryopreservation of germ cells before treatment.
* Individuals of child-bearing potential who are partners of male participants should be advised to use a highly effective method of contraception during the intervention period and for at least 11 months after the last dose of study intervention for the male participant
* Male participants (as assigned at birth) with a pregnant or breastfeeding partner must agree to remain abstinent from sexual activity or use a male condom during any sexual activity (eg, vaginal, anal, oral), even if the participant has undergone a successful vasectomy, during the intervention period and for at least 11 months after the last dose of study intervention
* Breastfeeding partners of male participants (as assigned at birth) should be advised to consult their health care provider about using appropriate highly effective contraception during the time the male participant is required to use condoms
* Recovery from the adverse effects of prior therapy at the time of enrollment to baseline or ≤ Grade 1 (excluding alopecia, peripheral neuropathy, and parameters superseded by other eligibility criteria \[eg, hematology parameters\]). Note: Participants with prior endocrine adverse effects are permitted to enroll if they are stably maintained on appropriate replacement therapy and are asymptomatic.
* Required organ function
* Adequate hematologic function defined as follows:
* Absolute neutrophil count (ANC) ≥ 1,500 cells/mm\^3
* Platelets ≥ 100,000 cells/mm3
* Hemoglobin ≥ 8 g/dl
* Adequate renal function defined as follows:
* Creatinine clearance (CrCL) of ≥50 mL/min by the CKD-Epi creatinine equation
* Adequate hepatic function defined as follows:
* Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) (patients with known Gilbert's disease who have bilirubin level ≤ 3 x ULN may be enrolled)
* AST and ALT ≤5 x ULN
* Signed informed consent form (ICF)

Exclusion Criteria:

* Prior treatment with PRMT5i or MAT2Ai
* Symptomatic CNS metastases
* Patients with treated brain metastases are eligible if follow up brain imaging after CNS directed therapy shows no evidence of progression and the patient is on a stable dose of corticosteroids
* Received palliative radiation therapy within 3 days prior to initiation of study treatment or definitive SRS including CNS SRS within 14 days prior to initiation of study treatment
* Patients who have had major surgery within 3 weeks of start of study drug

  o Note: procedures such as biopsy, pleural catheter insertion, central venous catheter or other minor procedures are permitted
* Any of the following cardiac abnormalities:
* Unstable angina pectoris or myocardial infarction within 6 months prior to enrollment
* Congestive heart failure ≥ NYHA Class 3 within 6 months prior to enrollment
* Prolonged QTc \> 500 milliseconds or history of Long QT Syndrome
* Child-Pugh class C liver cirrhosis
* Ongoing medical illness not otherwise listed which would preclude study at the discretion of the PI
* Inability to take medications PO (BMS-986504 cannot be taken via gastrostomy tube), refractory nausea and vomiting, malabsorption, biliary shunt, significant bowel resection, or any other condition that significantly affects gut motility or absorption and would preclude adequate absorption of BMS-986504 in the opinion of the treating physician and/or PI
* Ongoing need for a medication that is a strong inhibitor or strong inducer of cytochrome P450 (CYP) 3A4 and/or P-glycoprotein (P-gp) or proton-pump inhibitor that cannot be switched to alternative treatment prior to study entry
* HIV, HBV, or HCV with detectable viral load
* For patients with known HIV, HBV, and/or HCV infection:
* HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial.
* For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable with or without suppressive therapy
* Patients with a history of HCV infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load.
* Active infection requiring parenteral antibiotic(s)
* Pregnant or breastfeeding
* Presence of another malignancy that could be mistaken for the malignancy under study during disease assessments.
* Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial.

Inclusion Criteria:

* Pathologically confirmed recurrent or relapsed advanced ovarian cancer, primary peritoneal cancer, fallopian tube cancer, cholangiocarcinoma, or epithelial mesothelioma (pleural or peritoneal) after at least 1 prior line of systemic therapy for advanced disease
* Adult 18 years of age or older.
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1.
* Has at least 1 measurable lesion by iRECIST for ovarian cancer or cholangiocarcinoma or lesions measurable for mRECIST for mesothelioma.
* Satisfactory Blood coagulation parameters
* Satisfactory organ and bone marrow function

Exclusion Criteria:

* Active invasive cancers other than mesothelioma, cholangiocarcinoma, and ovarian unless surgically and medically cured without evidence of recurrent disease for 5 years.
* History of T or B cell malignancies or previous gene-engineered T cell therapies.
* Sarcomatoid/biphasic mesothelioma.
* Pulmonary exclusions
* Have acquired hereditary, congenital immunodeficiency or have recognized immunodeficiency disease
* Active hepatitis B, active hepatitis C, or any HIV infection at the time of screening
* Active autoimmune disease

* INCLUSION CRITERIA:

In order to be eligible to participate in this study, an individual must meet all of the following criteria. For this protocol, treatment initiation is defined as the first day of lymphodepleting chemotherapy.

* Participant must have unresectable, locally advanced, or metastatic, or recurrent mesothelioma and other mesothelin expressing solid tumors. For participants with mesothelioma only those with epithelioid or biphasic histology (with \>80% epithelioid component) will be eligible. The diagnosis will be confirmed by the Laboratory of Pathology, CCR, NCI.
* Participant must have progressed on at least one FDA-approved systemic therapy considered standard of care for their tumor type. There is no limit on the number of prior treatment regimens. Note: Given the aggressive nature of pancreatic cancer, otherwise eligible individuals with this cancer type can undergo leukapheresis before or while they are getting their frontline treatment as long as they meet all other inclusion criteria. However, TNhYP218 CAR T cells will only be administered after progression on first line standard of care therapy.
* Participant must have at least 1 measurable lesion by RECIST version 1.1.
* Tumor must have MSLN positivity of 2+ to 3+ in \>= 50% cancer cells by immunohistochemistry on freshly collected biopsy or archival tissue.
* Age \>= 18 years.
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
* Participants must have adequate organ and marrow function as defined below:

System: Laboratory Value

Hematological

* Hemoglobi: \>=9 g/dL(a)
* absolute neutrophil count: \>=1,500/mcL
* platelets: \>=100,000/mcL

Hepatic

* total bilirubin: \<=2.5 X institutional ULN OR direct bilirubin ULN for participants with total bilirubin levels \>1.5 X ULN
* AST and ALT \<= 2.5 X institutional ULN (\<= 5 X ULN for participants with liver metastases)

Renal

* Creatinine OR: \<=1.5 X ULN OR
* Calculated(b) creatinine clearance (GFR can also be used in place of creatinine or CrCl) \>= 50 mL/min for participant with creatinine levels \> 1.5 X institutional ULN

Coagulation

* International normalized ratio (INR) OR prothrombin time (PT): \<=1.5 X ULN unless participant is receiving anticoagulant therapy if PT or aPTT is within therapeutic range of intended use of anticoagulants
* Activated partial thromboplastin time (aPTT): \<=1.5 X ULN unless participant is receiving anticoagulant therapy if PT or aPTT is within therapeutic range of intended use of anticoagulants

ALT (SGPT)=alanine aminotransferase (serum glutamic pyruvic transaminase); AST (SGOT)=aspartate aminotransferase (serum glutamic oxaloacetic transaminase); GFR=glomerular filtration rate; ULN=upper limit of normal.

1. Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks.
2. Creatinine clearance (CrCl) should be calculated per institutional standard.

   * Normal cardiac ejection fraction (\>= 45% by echocardiogram) and no evidence of hemodynamically significant pericardial effusion as determined by an echocardiogram.
   * Room air oxygen saturation of 90% or greater.
   * Treatment-related toxicities from prior treatments must be resolved to \<= grade 2.
   * Participants with CNS metastases, leptomeningeal disease or carcinomatous meningitis are eligible if they are asymptomatic, have completed their treatment for CNS disease and have recovered from the acute effects of radiation therapy or surgery prior to study entry. Participants must have radiographically stable CNS disease without associated edema at least three months prior to study entry. Additionally, participants have had to have discontinued corticosteroid treatment or non-prophylactic antiseizure medications for these metastases at least four weeks prior to study entry.
   * Participants of child-bearing potential and participants who can father children must agree to use highly effective contraception or abstinence.
   * Participants who are nursing or plan to nurse a child must agree to discontinue/postpone nursing for the duration of study therapy and for 12 months after the administration of the cell product or for 4 months from the time no evidence of persistence/gene modified cells is documented in the participant s blood.
   * Ability of participant to understand and the willingness to sign a written informed consent document.

   EXCLUSION CRITERIA:

   An individual who meets any of the following criteria will be excluded from participation in this study:
   * Prior systemic therapy, an investigational therapy, radiation, and/or surgery within 14 days prior to leukapheresis and 21 days prior to lymphodepleting chemotherapy.
   * Prior administration of anti-PD-1 or anti-PD-L1 antibodies or other agents that in the opinion of the PI can stimulate immune activity and interfere with an infusion of CAR-T cells within 8 weeks prior to treatment initiation.
   * Participants with any form of primary immunodeficiency (e.g. severe combined immunodeficiency).
   * Participants with active or history of autoimmune or immune mediated disease such as multiple sclerosis, lupus, inflammatory bowel disease, rheumatoid arthritis, or small vessel vasculitis. NOTE: Participants with vitiligo, endocrine deficiencies including thyroiditis managed with replacement hormones including physiologic corticosteroids are eligible.
   * History of severe immediate hypersensitivity reaction to cyclophosphamide or fludarabine.
   * Therapeutic doses of systemic corticosteroid therapy within 14 days prior to treatment initiation. Physiological doses of steroids (up to 5mg/day of prednisolone or equivalent) are allowed. Corticosteroid creams, ointments, and eye drops are allowed.
   * Participants with lung fibrosis, inflammatory lung disease or evidence of pneumonitis on baseline imaging studies or medical history of these disorders.
   * Participant has any other prior or concurrent malignancy with the following exceptions:

     * Adequately treated basal cell or squamous cell carcinoma
     * In situ carcinoma of the cervix or breast, treated curatively and without evidence of recurrence for at least 12 months prior to initiation of study therapy.
     * Treated non-melanoma skin cancer.
     * Stage 0 or 1 melanoma completely resected at least 12 months prior to initiation of study therapy.
     * Successfully treated organ-confined prostate cancer with no evidence of progressive disease based on PSA levels and are not on active therapy.
     * A primary malignancy which has been completely resected and in complete remission for \>= 5 years.
   * Electrocardiogram showing a QTc interval \> 450 msec in males and \> 470 msec in females (\> 80 msec for participants with bundle branch block). Either Fridericia s or Bazett s formula may be used to correct the QT interval.
   * Participant has active infection with HIV, hepatitis B virus, HCV, or HTLV as defined below:

     * Positive serology for HIV, HTLV-1, or HTLV-2.
     * Active hepatitis B infection as demonstrated by test for hepatitis B surface antigen. Participants who are hepatitis B surface antigen negative but are hepatitis B core antibody positive must have undetectable hepatitis B DNA and receive prophylaxis against viral reactivation.
     * Active hepatitis C infection as demonstrated by hepatitis C RNA test. Participants who are HCV antibody positive will be screened for HCV RNA by any reverse transcription PCR or branched DNA assay. If HCV antibody is positive, eligibility will be determined based on a negative screening RNA value.
   * Participant is pregnant or intends to be pregnant during the required period of contraception for participants of childbearing potential.
   * Participants who received live or attenuated vaccine or virus-based vaccine within 30 days before initiation of treatment initiation
   * Participants with a history of seizure disorder unless due to now treated metastatic lesions.
   * Ongoing uncontrolled intercurrent illness, including but not limited to ongoing or active infection, that would impact participant safety or limit compliance with study requirements.