Intraperitoneal FT536 in Recurrent Ovarian, Fallopian Tube, and Primary Peritoneal Cancer

Inclusion Criteria: * Recurrent epithelial ovarian cancer, fallopian tube, or primary peritoneal cancer meeting one of the following minimal prior treatment requirements (no limit to the maximum number of prior treatments). * Must have received prior bevacizumab. * In the presence of a BRCA mutation, must have received a prior PARP inhibitor. * Adequate organ function within 14 days (28 days for pulmonary and cardiac) of study treatment (CY/Flu) start * Agrees to the placement of an intraperitoneal catheter before the 1st dose of study directed drug (chemotherapy) and remains in place through Day 36 or longer if retreatment is planned. Refer to Section 6.4 if catheter cannot be successfully placed. * Agrees to undergo a tumor biopsy if feasible at the time the catheter is placed and removed - Accessible tumor for biopsy is not required for eligibility * Must agree to and sign the consent for the companion Long-Term Follow-Up study (CPRC# 2021LS077) to fulfill the FDA recommended 15 years of followup for a genetically modified cell product. Exclusion Criteria: * Pregnant or breastfeeding or planning on becoming pregnant in the next 6 months. If of childbearing potential (have a uterus and ovaries) and engaged in heterosexual intercourse, must have a negative pregnancy test (serum or urine) within 14 days before the 1st CY/Flu. Patient must agree to use highly effective method of birth control from the screening visit until at least 12 months after the final dose of CY, or a…