General Inclusion Criteria:  Participants must have a histological diagnosis of metastatic or recurrent high-grade serous ovarian cancer, which includes fallopian tube, or primary peritoneal cancer.  General Exclusion Criteria:  Participant is unable or unlikely to comply with dosing schedule and study evaluations.  UPGRADE-A Combination-specific Inclusion Criteria:  Participant has received 1 to 2 prior lines of platinum-containing chemotherapy for their ovarian cancer. They must have platinum-sensitive recurrent disease Participant must have an ECOG performance status 0 or 1 Participant must have measurable or evaluable disease as per RECIST v1.1 Tumor sample must be provided, either an archival tumor tissue block or slides or, if not available, a tumor tissue block or slides from a new tumor biopsy obtained through a low-risk, medically routine procedure. Participants with toxicity from prior therapy or surgical procedures must have recovered to ≤ Grade 1. Participants with alopecia, stable immune-related toxicity such as hypothyroidism on hormone replacement, adrenal insufficiency treated with ≤10 mg daily prednisone (or equivalent), or chronic Grade 2 peripheral sensory neuropathy after prior taxane therapy is an exception to this criterion and may qualify for this study. Participants must have cardiac left ventricular ejection fraction (LVEF) ≥50% or ≥ the institution's lower limit of normal as measured by either Echo or MUGA scan Participants must have adequate organ function within 14 days prior to enrollment A female participant is eligible to participate if she is not pregnant or breastfeeding, if she is not a woman of childbearing potential, or if she is a woman of childbearing potential and using a contraceptive method that is highly effective.  UPGRADE-A Combination-specific Exclusion Criteria:  Participant has a prior hypersensitivity reaction to carboplatin requiring desensitization or discontinuation. Participant has prior platelet or neutrophil toxicity to carboplatin-containing therapy requiring dose reduction to AUC <5. Participant has had major surgery within 28 days of starting study treatment, systemic anticancer therapy within the lesser of 28 days or 5 half-lives of the prior therapy before starting study treatment (14 days or 5 half-lives for small molecule targeted therapy), or recent radiation therapy with unresolved toxicity or within a time window of potential toxicity Participant has received prior treatment with mirvetuximab soravtansine or another ADC containing an auristatin or maytansinoid payload. Participant has untreated CNS metastases (including new and progressive brain metastases), history of leptomeningeal metastasis, or carcinomatous meningitis. Has a diagnosis of additional malignancy that required treatment within 2 years prior to screening, except for adequately treated basal cell or squamous cell skin cancer, or carcinoma in situ of the breast or of the cervix Participant is unwilling to be transfused with blood components. Participant is receiving concurrent anti-cancer therapy (e.g. chemotherapy, radiation therapy, biologic therapy, immunotherapy, hormonal therapy, investigational therapy).