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).