A Two-Part Phase 3 Study of Sofetabart Mipitecan (LY4170156) in Participants With Platinum-Resistant (Part A) and Platinum-Sensitive (Part B) Ovarian Cancer

Inclusion Criteria: Part A and B: * Have histologically confirmed high-grade serous or high-grade endometrioid ovarian, primary peritoneal, or fallopian tube cancer. * Have confirmed availability of tumor tissue block or slides * Have radiographic progression on or after most recent line of systemic anticancer therapy * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1. * Have measurable disease per RECIST v1.1 Part A: * Have platinum-resistant disease, defined as radiographic progression less than or equal to (≤)6 months of the last administration of platinum therapy. * Have previously received greater than or equal to (≥)1 but ≤3 prior lines of systemic cytotoxic therapy. Up to 4 lines of prior therapy is allowed if one of those lines is mirvetuximab soravtansine. * Have received prior bevacizumab treatment, unless documented contraindication or intolerance. * Have received treatment with a poly(ADP-ribose) polymerase inhibitor (PARPi) if known to have a somatic or germline breast cancer gene (BRCA) mutation, if clinically indicated, unless documented contraindication or intolerance. Part B: * Have relapsed after first-line platinum-based chemotherapy and have platinum-sensitive disease defined as radiographic progression greater than (\>)6 months of their last administration of platinum therapy * Have previously received ≥1 but ≤2 prior lines of systemic cytotoxic chemotherapy * Have previously received a PARPi, per local product label, with progression on, or within 6 months of completion of PARPi treatment. Exclusion Criteria: Part A and B: \- Have received prior antibody-drug conjugate (ADC) with a topoisomerase inhibitor payload. Part A: \- Have primary platinum-refractory disease, defined as disease that progressed ≤3 months since the last dose of first-line platinum-containing chemotherapy. Part B: \- Have clinically significant proteinuria