MOv19-BBz CAR T Cells in aFR Expressing Recurrent High Grade Serous Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria: 1. Histologically confirmed persistent or recurrent stage II to IV high grade serous epithelial ovarian, fallopian tube or primary peritoneal carcinoma. Disease can be platinum-sensitive or platinum-resistant. 2. Failure of at least two prior chemotherapy regimens for advanced stage disease. Prior therapies against PD-1 or PDL-1 are permissible. 3. Confirmation of tumor aFR expression (≥70% of tumor cells with ≥2+ aFR staining). 4. Subjects must have measureable disease as defined by RECIST 1.1 criteria. 5. Patients with asymptomatic CNS metastases that have been treated and are off steroids are allowed. They must meet the following at the time of eligibility confirmation by physician-investigator: 1. No concurrent treatment for the CNS disease 2. No progression of CNS metastasis on brain MRI at screening 3. No evidence of leptomeningeal disease or cord compression 6. Patients ≥ 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: i. Absolute neutrophil count ≥ 1,000/μl ii. Platelets ≥75,000/μl iii. Hemoglobin ≥ 9 g/dL iv. Total bilirubin ≤ 2.0x the institutional normal upper limit unless secondary to bile duct obstruction by tumor v. Creatinine ≤ 1.5x the institutional normal upper limit vi. Albumin ≥2 vii. Serum alanine aminotransferase (ALT) or aspartate aminotransferase (AST) ≤ 5x the institutional normal upper limit viii. Cardiac ejection fraction of ≥40% 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. Provides written informed consent. 11. Subjects of reproductive potential must agree to use acceptable birth control methods, as described in protocol Section 4.3. Exclusion Criteria: 1. High grade serous ovarian, fallopian, or primary peritoneal cancer that is platinum refractory, defined as disease that has clinical or radiographic progression on platinum-based chemotherapy, as per the discretion of the treating physician. 2. Patients with symptomatic CNS metastases are excluded. 3. Participation in a therapeutic investigational study within 4 weeks prior to eligibility confirmation by physician-investigator, or anticipated treatment with another investigational product while on study. This refers to non-commercially approved investigational drugs different than those used in this protocol. 4. Active invasive cancer other than ovarian cancers. Patients with active non-invasive cancers (such as non-melanoma skin cancer, superficial cervical and bladder cancer) are not excluded. 5. HIV infection 6. Hepatitis B or hepatitis C infection 7. Active autoimmune disease requiring systemic immunosuppressive treatment equivalent to \>/= 10 mg of prednisone. Patients with autoimmune neurologic diseases (such as multiple sclerosis) will be excluded. 8. Patients with active and uncontrolled infection. 9. Planned concurrent treatment with systemic high dose corticosteroids. Patients may be on a stable low dose of steroids (\<10 mg daily equivalent of prednisone). Corticosteroids treatment as anti-emetic prophylaxis on the day of lymphodepleting chemotherapy administration is allowed per institutional guidance. The use of topical and/or inhaled steroids are not exclusionary. 10. Patients requiring supplemental oxygen therapy. 11. Prior therapy with lentiviral gene modified cells. 12. History of allergy or hypersensitivity to study product excipients (human serum albumin, DMSO, and Dextran 40). 13. Any ascites requiring therapeutic drainage within 4 weeks prior to eligibility confirmation by physician-investigator. 14. Pregnant or breastfeeding women. 15. Presence of any other condition that may increase the risk associated with study participation or may interfere with the interpretation of study results, and, in the opinion of the physician-investigator, would make the patient inappropriate for entry into the study.