Modified Immune Cells (Autologous CAR T Cells) in Treating Patients with Advanced, Recurrent Platinum Resistant Ovarian, Fallopian Tube or Primary Peritoneal Cancer

Inclusion Criteria: * Women with recurrent, advanced, platinum resistant ovarian, fallopian tube, and primary peritoneal cancer that have progressed after receiving standard of care therapies or are not eligible to receive available therapies with known clinical benefit will be eligible for the study. Patients must have measurable disease that can be accurately measured by RECIST 1.1 criteria in at least one dimension as \>= 1.0 cm or \> 1.5 cm lymph node with computed tomography (CT), ultrasound, or magnetic resonance imaging (MRI) techniques. * Platinum resistant is defined as progression of disease within six months of platinum regimen. * Patients with BRCA mutations who have completed standard therapies (including PARP inhibitors) are allowed on this study. * Patients must be capable of understanding and providing a written informed consent. * Patients must be 14 days from previous cytotoxic chemotherapy at time of cell collection. * Laboratory values must indicate adequate organ function. * Patients must be at least 28 days post systemic steroids prior to enrollment except as premedication for contrast allergy and/or other protocol-mandated medication. * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status score of =\< 2. * Patients must have recovered from major acute infections and/or recent surgical procedures, and in the opinion of the investigator, not have any significant active concurrent medical illnesses precluding protocol treat…