* INCLUSION CRITERIA:

Patients 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.

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

Patients must be 2 years of age or older. Note: Patients \>= 2 and \< 18 years of age may participate in research sample collection if the tissue acquisition is performed during a clinically indicated surgical procedure, and the sampling of tissue, blood and urine does not add risk to the clinically indicated procedures.

Patients must be aware of the nature of his/her illness. The patient must be willing to undergo standard intervention that may include endoscopic biopsies of tumor and adjacent normal tissues, and to provide blood and urine samples to support ongoing laboratory research endeavors pertaining to the epigenetics of thoracic malignancies.

Ability of subject, 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 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

* 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:

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.

Inclusion Criteria:

* ECOG 0 or 1
* Subjects with evaluable disease per RECIST 1.1 or mRECIST
* Subjects with adequate organ function.
* Subjects with advanced cancers associated with mesothelin expression

Exclusion Criteria:

* Uncontrolled significant active infection or any medical or other condition that in opinion of the investigator would preclude the subject's participation in the study.
* Prior treatment with MSLN-targeted CD3 or chimeric antigen receptor T cell (CAR-T) therapy
* Concurrent participation in another investigational clinical trial.
* Evidence of leptomeningeal disease

Inclusion Criteria:

Key Inclusion Criteria:

1. Appropriately enrolled in the BASECAMP-1 A2 Biotherapeutics, Inc. study, with tissue demonstrating LOH of HLA-A\*02 by NGS (whenever possible from the primary site), successful apheresis and PBMC processing, and with sufficient stored cells available for Tmod CAR T-cell therapy
2. Histologically confirmed recurrent unresectable, locally advanced, or metastatic CRC, NSCLC, PANC, OVCA, MESO, or other solid tumors with MSLN expression. Measurable disease is required with lesions of ≥1.0 cm by CT.
3. Received previous required therapy for the appropriate solid tumor disease as described in the protocol
4. Has adequate organ function as described in the protocol
5. ECOG performance status of 0 to 1
6. Life expectancy of ≥3 months
7. Willing to comply with study schedule of assessments including long term safety follow up

Key Exclusion Criteria:

1. Has disease that is suitable for local therapy or able to receive standard of care therapy that is therapeutic and not palliative
2. Prior allogeneic stem cell transplant
3. Prior solid organ transplant
4. MESO with pleural involvement extending into the peritoneum
5. Cancer therapy within 3 weeks or 3 half lives of infusion
6. Radiotherapy within 28 days of infusion
7. Unstable angina, arrhythmia, myocardial infarction, or any other significant cardiac disease within the last 6 months
8. Any new symptomatic pulmonary embolism (PE) or a deep vein thrombosis (DVT) within 3 months of enrollment. Therapeutic dosing of anticoagulants is allowed for history of PE or DVT if greater than 3 months from time of enrollment, and adequately treated
9. History of interstitial lung disease including drug-induced interstitial lung disease and radiation pneumonitis that requires treatment with prolonged steroids or other immune suppressive agents within 1 year
10. Requires supplemental home oxygen
11. Females of childbearing potential who are pregnant or breastfeeding
12. Subjects, both male and female, of childbearing potential who are not willing to practice birth control from the time of consent through 6 months post infusion

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:
* 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.

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:

* 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:

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.

Key Eligibility Criteria (additional criteria may apply) Part 1 Key Inclusion Criteria

1\. Pathologically confirmed solid tumors, e.g., Colorectal Cancer (CRC), Non-Small Cell Lung Cancer (NSCLC), or Pancreatic Cancer (PANC), that is metastatic, unresectable locally advanced, or in the Investigator's opinion the subject is high risk for incurable relapse within two years.

Part 1: Key Exclusion Criteria

1. History of any of other malignancy in the past 5 years other than non-melanoma skin carcinoma, low grade localized prostate cancer, superficial bladder cancer, ductal carcinoma in situ (CIS) of the breast, CIS of the Cervix, or Stage I uterine cancer.
2. Prior allogeneic stem cell transplant.
3. Prior solid organ transplant.

Part 2 : Key Inclusion Criteria

1. Pathologically confirmed solid tumors, e.g., Colorectal Cancer (CRC), Non-Small Cell Lung Cancer (NSCLC), Pancreatic Cancer (PANC), Mesothelioma, or Ovarian Cancer (OVAC) that is metastatic, unresectable locally advanced, or in the Investigator's opinion the subject is high risk for incurable relapse within two years.
2. Participants are germline HLA-A\*02 heterozygous confirmed by HLA typing.
3. Primary tumor tissue showing LOH of HLA-A\*02 by NGS testing.
4. Eastern Cooperative Oncology Group (ECOG) 0 or 1 performance status.

Part 2: Key Exclusion Criteria

1. History of any of other malignancy in the past 5 years other than non-melanoma skin carcinoma, low grade localized prostate cancer, superficial bladder cancer, ductal carcinoma in situ (CIS) of the breast, CIS of the Cervix, or Stage I uterine cancer.
2. Prior allogeneic stem cell transplant.
3. Prior solid organ transplant.
4. Participants who have received any cancer therapy on any investigational therapy for any indication, including but not limited to chemotherapy, small molecules, monoclonal antibodies, or radiotherapy (with bone marrow impact) within 2 weeks of planned apheresis or 3 half-lives, whichever is shorter.
5. Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of nail beds) at study enrollment necessitating specific treatment, or any major episode of infection requiring treatment with Intravenous (IV) antimicrobials (e.g., IV antibiotics) or hospitalization (relating to completion of antibiotic course).
6. Has known active central nervous system metastases. Subjects with previously treated brain metastases may participate upon medical monitor agreement.
7. In the Investigator's judgement, any other condition or reason the subject would not complete the required study visits and procedures, and follow up visits, or comply with the study requirements for participation.

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

Inclusion Criteria:

* Patient, or legally authorized representative (LAR), willing and able to provide written informed consent for the trial
* Patient age ≥ 18 at time of consent
* Pathologically confirmed diffuse pleural mesothelioma
* Must have received at least one prior systemic therapy (platinum/pemetrexed, immunotherapy or a combination thereof)
* Measurable disease as defined primarily by the modified RECIST criteria for mesothelioma (at PI discretion RECIST v1.1 may be used)
* Consent to undergo a biopsy prior to Cycle 1 Day 1 and Cycle 3 Day 1 if deemed medically safe and feasible
* Eastern Cooperative Oncology Group (ECOG) score 0 or Karnofsky Performance Status ≥ 70%
* Adequate organ function, defined as

  * Absolute neutrophil count ≥ 1.5K/mcL
  * Platelet count ≥ 100K/mcL
  * Adequate renal function defined as creatinine clearance ≥ 30ml/min (as calculated by Cockcroft-Gault Formula)
  * Hemoglobin \> 9g/dL (prior transfusion permitted if not within 7 days of enrollment)
  * Total bilirubin ≤1.5 x upper limit of normal (ULN) if no liver metastases or \<3 × ULN in the presence of documented Gilbert's Syndrome (unconjugated hyperbilirubinemia) or liver metastases; subjects with Gilbert's syndrome can enroll if conjugated bilirubin is within normal limits
  * AST, ALT ≤ 2.5 x ULN (if liver metastases are present, ≤5 × ULN)
* If of childbearing potential, must be willing to use highly effective mode of contraception for at least one month prior, during, and for 2 months after the end of active therapy

Exclusion Criteria:

* Currently participating in another study and receiving another study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 3 weeks of the first dose of treatment
* Prior hypersensitivity to irinotecan or any components of sacituzumab govitecan-hziy
* Prior cytotoxic/immunologic systemic therapy within 3 weeks prior to study Day 1 or has not recovered (i.e., CTCAE v5 ≥ Grade 1 at baseline; from clinically significant adverse events due to a previously administered agent (excluding Grade 2 neuropathy)
* Known psychiatric or substance abuse disorders that would interfere with the requirements of the trial within the opinion of the investigator
* Known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, early stage prostate cancer, or in situ cervical cancer after definitive treatment
* Positive hepatitis B (hepatitis B virus \[HBV\]) surface antigen (HBsAg)

  o NOTE: Subjects with a prior history of HBV demonstrated by positive hepatitis B core antibody are eligible if they have at Screening 1) a negative HBsAg and 2) a HBV DNA (viral load) below the lower limit of quantification, per local testing. Patients who fit these criteria must use Hep B prophylaxis during treatment. Subjects with a positive HBsAg due to recent vaccination are eligible if HBV DNA (viral load) is below the lower limit of quantification, per local testing
* Positive hepatitis C antibody (anti-HCV)

  o NOTE: Subjects with a prior history of HCV, who have completed antiviral treatment and have subsequently documented HCV RNA below the lower limit of quantification per local testing are eligible
* Participant is positive for human immunodeficiency virus (HIV), with 1 or more of the following:

  * Receiving ART that may interfere with study treatment (consult sponsor for review of medication prior to enrollment)
  * CD4 count \< 350 cells/mm3 at screening
  * AIDS-defining opportunistic infection within 6 months of start of screening
  * Not agreeing to start ART and be on ART \> 4 weeks plus having HIV viral load \<400 copies/mL at end of 4-week period (to ensure ART is tolerated and HIV controlled)
* Myocardial infarction, unstable angina, stroke, transient ischemic attack (TIA), or coronary/peripheral artery bypass graft, or any acute coronary syndrome within 6 months of start of study drug
* Congestive heart failure defined as New York Heart Association (NYHA) Class III-IV or hospitalization for congestive heart failure (any NYHA class) within 6 months of study Day 1
* Pregnant women or women who are breastfeeding or of childbearing potential and not using a highly effective method of birth control for at least one month prior to enrollment. If the risk of contraception exists, male and female subjects must use highly effective contraception throughout the study and for at least 60 days after last treatment. Highly effective contraception includes either 2 barrier methods (diaphragm, condom by the partner, copper intrauterine device, sponge, or spermicide), or 1 barrier method and 1 hormonal method (any oral, subcutaneous, intrauterine, or intramuscular registered and marketed contraceptive agent that contains an estrogen and/or a progesterone agent)

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:
* Histologically confirmed pancreatic ductal adenocarcinoma (PDAC), cholangiocarcinoma, hepatocellular carcinoma (HCC), gastric cancer, bladder cancer, ovarian cancer, pheochromocytoma/paraganglioma (PPGL), small cell lung cancer (SCLC) or extrapulmonary neuroendocrine cancer (EP-NEC), mesothelioma or sarcoma.
* Participants must be scheduled or intended to receive treatment for their cancer.
* Evaluable disease
* \>= 18 years old.
* Eastern Cooperative Oncology Group (ECOG) performance score \<= 2.
* Individuals of child-bearing potential (IOCBP) and individuals that can father children must agree to use effective contraception (barrier, hormonal, intrauterine device (IUD), surgical sterilization, abstinence) at the study entry and for 2 months after each (18F) FAPI-74 imaging. Sperm may not be frozen or donated within the same period.
* Must be willing to discontinue breastfeeding for 2 months after each study imaging.
* The ability of participant to understand and the willingness to sign a written informed consent document.

EXCLUSION CRITERIA:

* History of allergic reactions attributed to compounds of similar chemical or biologic composition to \[18F\]FAPI-74 or other agents used in the study.
* History of severe claustrophobia unresponsive to oral anxiolytics or history of any other condition preventing the ability to lie on the imaging scanner for up to 45 minutes.
* Weight \> 350 lbs., or inability to fit within the imaging gantry.
* Positive Beta-human chorionic gonadotropin (Beta-HCG) serum or urine pregnancy test performed in IOCBP at screening.
* Uncontrolled intercurrent illness, or medical condition(s) including but not limited to renal failure, liver failure, or psychiatric illness/social situations evaluated by medical history and physical exam that would limit compliance with study requirements and potentially increase risk for the participant.
* Serum creatinine \> 2 times the upper limit of normal.
* Liver transaminases (ALT, AST) greater than 3 times the upper limit of normal.

Inclusion Criteria:

* Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care
* Female subject is either: a. post-menopausal for at least one year before the screening visit; or b. surgically sterilized; or c. willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study and at least 6 months after the last dose of brentuximab vedotin
* Male subject, even if surgically sterilized (i.e., status postvasectomy), agrees to use an acceptable barrier method for contraception (condom with a spermicidal agent), or completely abstain from heterosexual intercourse during the entire study treatment period through 6 months after the last dose of brentuximab vedotin
* Absolute neutrophil count (ANC) \> 1500/mm\^3
* Platelets \> 100,000/mm\^3
* Hemoglobin (Hgb) \> 8.5 g/dL
* Total bilirubin =\< 1.5 x upper limit of normal (ULN)
* Serum glutamic-oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) \< 3 x ULN; AST and/or ALT may be up to 5 X ULN if with known liver metastases (mets)
* Calculated creatinine clearance must be \>= 30 mL/minute
* Eastern Cooperative Oncology Group (ECOG) performance status 0-2
* Pathologic diagnosis of malignant mesothelioma (any primary site is acceptable, any histology is acceptable)
* Have unresectable malignant mesothelioma (any histology)
* Positive CD30+ immunohistochemical expression
* Any line of prior therapy - patients may be chemo-naive or chemo-refractory (any line)
* Patients must have measurable disease by modified Response Evaluation Criteria in Solid Tumors (RECIST) or RECIST; examinations for assessment of measurable disease must have been completed within 28 days prior to registration

Exclusion Criteria:

* Radiation therapy to more than 25% of the bone marrow; whole pelvic radiation is considered to be over 25%
* Prior allogeneic bone marrow or organ transplantation
* Female subject who is pregnant or breast-feeding; confirmation that the subject is not pregnant must be established by a negative serum beta-human chorionic gonadotropin (B-hCG) pregnancy test result obtained during screening; pregnancy testing is not required for post-menopausal or surgically sterilized women
* Patient has received other investigational drugs with 14 days before enrollment
* Serious medical or psychiatric illness likely to interfere with participation in this clinical study
* No prior history of malignancy within 2 years, unless cured of a skin cancer or a stage I-III solid tumor; no prior hematologic malignancy within 3 years
* Known hypersensitivity to brentuximab vedotin components
* Persons who are incarcerated at time of enrollment (e.g., prisoners) or likely to become incarcerated during the study

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

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

* 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