This is a clinical study that has three parts. It is testing a potential new medicine called Sofetabart Mipitecan (Sofe-M) for people with certain types of ovarian, peritoneal, and fallopian tube cancers. Part A enrolls participants with platinum-resistant cancer, meaning their disease progressed during or within six months of platinum-based chemotherapy. Parts B and C enroll participants with platinum-sensitive cancer, whose disease responded and remained controlled for at least six months after completing platinum treatment. The researchers want to find out if Sofe-M works better than the standard treatments that doctors use now and to better understand how safe it is. Each participant's time in the study will depend on how they respond to the treatment.

Inclusion Criteria:

Part A, B, and C:

• Have histologically confirmed high-grade serous or 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 1 to 3 prior lines of systemic cytotoxic therapy. Up to 4 lines of prior cytotoxic 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 and C:

• 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 to 2 prior lines of systemic cytotoxic chemotherapy

Part B:

- Have previously received a PARPi, per local product label, with progression on, or within 6 months of completion of PARPi treatment.

Part C:

- Have not previously received a PARPi treatment.

Exclusion Criteria:

Parts A, B and C:

- Have received prior antibody-drug conjugate (ADC) with a topoisomerase inhibitor payload.

Part A:

• Have primary platinum-refractory disease, defined as radiographic progression ≤ 1 month since the last dose of first-line platinum-containing chemotherapy.

Part B and C:

- Have clinically significant proteinuria

Part C:

- Have a known pathogenic BRCA1/2 gene alteration (somatic or germline).

Anonymized individual patient level data will be provided in a secure access environment upon approval of a research proposal and a signed data sharing agreement.

Data are available 6 months after the primary publication or approval of the indication studied in the US and EU, whichever is later. Data will be indefinitely available for requesting.

A research proposal should be approved by an independent review panel and researchers should sign a data sharing agreement.