CAR T Cells in Mesothelin Expressing Cancers

Inclusion Criteria 1. Histologically confirmed cancer (one of the following): 1. Cohorts 1-4 and Cohort 6 participants: \*\*Note: Cohorts 3 and 4 permanently closed\*\* * Metastatic or recurrent lung adenocarcinoma. * Persistent or recurrent serous epithelial ovarian cancer or primary peritoneal carcinoma or fallopian tube carcinoma * Malignant pleural and peritoneal mesothelioma (histologically confirmed epithelial) 2. Cohort 5 participants: \*\*Note: As of 1-Feb-2021 lung adenocarcinoma patients are no longer being enrolled in this trial\*\* * Metastatic or recurrent lung adenocarcinoma with documented pleural effusion * Persistent or recurrent serous epithelial ovarian cancer or primary peritoneal carcinoma or fallopian tube carcinoma with documented pleural effusion * Malignant pleural and peritoneal mesothelioma (histologically confirmed epithelial) with documented pleural effusion 3. Cohort 7 patients: * Persistent or recurrent serous epithelial ovarian cancer or primary peritoneal carcinoma or fallopian tube carcinoma with evidence of ascites * Malignant peritoneal mesothelioma (histologically confirmed epithelial) 2. CRITERIA HAS BEEN RETIRED 3. Failure of at least one prior standard of care chemotherapy for advanced stage disease. ALLOWANCE FOR PRIOR PD-1 or PDL-1 THERAPIES REMOVED. 4. Patients must have measurable disease as defined by RECIST 1.1 criteria or modified RECIST criteria (mesothelioma only). 5. Subjects with asymptomatic CNS metastases that have been treated (and are off steroids for the treatment of CNS disease) are allowed. They must meet the following at the time of enrollment: 1. No concurrent treatment for the CNS disease 2. No progression of CNS metastasis on MRI at screening scans 3. No evidence of leptomeningeal disease or cord compression 6. Subjects ≥ 18 years of age. 7. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. 8. Satisfactory organ and bone marrow function as defined by the following: * Absolute neutrophil count ≥ 1,000/μl * Platelets ≥75,000/μl * Hemoglobin ≥ 8 g/dL * Direct bilirubin ≤ 2.0 mg/dl unless secondary to bile duct obstruction by tumor or Gilbert's syndrome with a direct bilirubin of less that 3.0 mg/dl is allowed. * Creatinine ≤ 1.5x the institutional normal upper limit * Albumin ≥ 2 * Serum alanine aminotransferase (ALT) or aspartate aminotransferase (AST) ≤ 5x the institutional normal upper limit * Cardiac ejection fraction of ≥40% as measured by resting echocardiogram, with no clinically significant pericardial effusion. 9. Blood coagulation parameters: PT such that international normalized ratio (INR) is ≤ 1.5 and a PTT ≤ 1.2 time the upper limit of normal unless the patient is therapeutically anti-coagulated for history of cancer-related thrombosis and has stable coagulation parameters. 10. Provide written informed consent. 11. Subjects of reproductive potential must agree to use acceptable birth control methods. Exclusion Criteria 1. Sarcomatoid and biphasic mesothelioma. 2. Known leptomeningeal carcinomatosis or spinal cord compression. Screening for this is not required unless suspicious symptoms. 3. Subjects with symptomatic CNS metastases are excluded. 4. EXCLUSION CRITERIA HAS BEEN RETIRED 5. Active invasive cancer other than the one of the three cancers in this study. Subjects with active non-invasive cancers (such as non-melanoma skin cancer, superficial cervical and bladder and prostate cancer with PSA level \< 1.0) are not excluded. 6. HIV infection 7. Active hepatitis B or hepatitis C infection 8. Active autoimmune disease (including but not limited to: systemic lupus erythematosus, Sjogren's syndrome, rheumatoid arthritis, psoriasis, multiple sclerosis, inflammatory bowel disease, etc.) requiring immunosuppressive therapy within four (4) weeks prior to eligibility confirmation by physician-investigator, with the exception of thyroid replacement. 9. Patients with ongoing or active infection. 10. Dependence on systemic steroids or immunosupressant medications. 11. Patients requiring supplemental oxygen therapy. 12. Prior therapy with lentiviral gene modified cells. 13. History of allergy or hypersensitivity to study product excipients (human serum albumin, DMSO, and Dextran 40) 14. Any clinically significant pericardial effusion, Class II-IV cardiovascular disability according to the New York Heart Association Classification or other cardiovascular condition that would preclude assessment of mesothelin induced pericarditis, or which may worsen as a result of expected toxicities in this study. This determination will be made by a cardiologist if cardiac issues are suspected. 15. Any clinically significant pleural or peritoneal effusion that cannot be drained with standard approaches. An indwelling drainage device placed prior to eligibility confirmation by physician / investigator is acceptable. 16. Pregnant or breastfeeding women. 17. EXCLUSION HAS BEEN RETIRED 18. EXCLUSION HAS BEEN RETIRED 19. Subjects with significant lung disease as follows: * Subjects with radiographic evidence of greater than lobar lymphangitic pulmonary involvement, greater than lobar bronchial wall thickening suggestive of peribronchial lymphatic disease extension, and/or evidence of extensive bilateral parenchymal metastatic burden. * Subjects with radiographic and/or clinical evidence of active radiation pneumonitis. * Subjects with radiographic evidence of underlying interstitial lung disease, including evidence of unresolved drug toxicity from any agent (e.g. chemotherapy, targeted agents, amiodarone, nitrofurantoin, etc.)