This Phase 1/2 study evaluates the safety, tolerability, and preliminary anti-tumor activity of dual-targeting chimeric antigen receptor natural killer (CAR-NK) cells in participants with recurrent or refractory epithelial ovarian, primary peritoneal, or fallopian tube cancer. At screening, each participant's tumor is assessed for expression of Mesothelin (MSLN), Folate Receptor alpha (FRalpha/FOLR1), and MUC16 (CA 125). Participants are assigned to the dual-target CAR-NK product that best matches their tumor antigen profile to reduce the risk of antigen escape.