Intraperitoneal Delivery of Adaptive Natural Killer (NK) Cells (FATE-NK100) With Intraperitoneal Int

This is a Phase I trial to determine the maximum tolerated dose/maximum feasible dose (MTD/MFD) of a single infusion of FATE-NK100 via intra-peritoneal catheter in women with recurrent ovarian, fallopian tube or primary peritoneal cancer meeting one of the following minimal prior treatment requirement: * Platinum resistant: may receive FATE-NK100 as 2nd line (as 1st salvage therapy). Platinum resistant is defined as disease that has responded to initial chemotherapy but demonstrates recurrence within a relatively short period of time (\< 6 months) following the completion of treatment. * Platinum sensitive: may receive FATE-NK100 as 3rd line therapy (as 2nd salvage therapy). Platinum sensitive is defined as the recurrence of active disease in a patient who has achieved a documented response to initial platinum-based treatment and has been off therapy for an extended period of time (≥ 6 months).