A Study to Assess Adverse Events and Change in Disease Activity of Multiple Treatment Combinations With Intravenous Mirvetuximab Soravtansine in Adult Participants With Ovarian Cancer

Ovarian cancer is a lethal disease with an estimated 310,000 new cases and 200,000 deaths experienced worldwide in 2020. The purpose of this study is to assess the adverse events and change in disease activity of mirvetuximab soravtansine with carboplatin, or bevacizumab (Bev), or bev alone in participants with ovarian cancer (OC). Participants must have confirmation of folate receptor alpha (FRa) positivity by the Ventana folate receptor 1 (FOLR1) Assay. Mirvetuximab Soravtansine (MIRV) is an investigational drug for the treatment of OC. Participants will be assigned to 1 of 3 substudies and further into groups called treatment arms. In substudy 1, arms A-C, participants will receive 1 of 2 doses of MIRV with Bev, or Bev alone. In substudy 2, arms D and E, participants will receive 1 of 2 doses of MIRV with carboplatin, followed by MIRV alone. In substudy 3, arms F and G, participants will receive one of two doses of MIRV with BEV and carboplatin, followed by MIRV with BEV. Approximately 400 participants will be enrolled in the study at 100 sites around the world. Participants will receive intravenously (IV) infused MIRV with IV infused carboplatin, or IV infused Bev, or IV infused carboplatin and Bev, or IV infused Bev alone. The total study duration will be approximately 40 months. There may be higher treatment burden for participants in this trial compared to their standard of care. Participants will attend regular visits during the study at a hospital or clinic and may require frequent medical assessments, blood tests, and scans.

Inclusion Criteria: Substudy 1 * Participants must be willing to provide an archival tumor tissue block or slides or must undergo a procedure to obtain a new tumor biopsy using a low-risk, medically routine procedure for immunohistochemistry (IHC) confirmation of FRα expression as defined by the central VENTANA FOLR1 (FOLR1-2.1) assay. Tumors must have FRα-expression in \>= 50% of viable tumor cells with \>= 2+ staining intensity. * Participants must have an Eastern Cooperative Oncology Group performance status of 0 or 1. * 1L participants must have a confirmed diagnosis of Federation of Gynecology and Obstetrics (FIGO) Stage III or IV high-grade serous epithelial ovarian, primary peritoneal, or fallopian tube cancer. 2L participants must have platinum-sensitive high-grade serous epithelial ovarian, primary peritoneal, or fallopian tube cancer. Participants must have platinum-sensitive disease defined as radiographic progression greater than 183 days from the last dose of most recent platinumbased chemotherapy. Note: Progression should be calculated from the date of the last administered dose of platinum therapy to the date of the radiographic imaging showing progression. * Participant has a local homologous recombination deficient (HRD) or breast cancer susceptibility gene (BRCA) test result available. Participants with BRCA wild-type will need to have a local HRD test result available. Substudy 2 * Participants must be willing to provide an archival tumor tissue block or slides or must undergo a procedure to obtain a new tumor biopsy using a low-risk, medically routine procedure for immunohistochemistry (IHC) confirmation of FRα expression as defined by the central VENTANA FOLR1 (FOLR1-2.1) assay. Tumors must have FRα-expression in \>= 50% of viable tumor cells with \>= 2+ staining intensity. * Participants must have an Eastern Cooperative Oncology Group performance status of 0 or 1. * Participants must have a confirmed diagnosis of high-grade serous ovarian, primary peritoneal, or fallopian tube cancer. * Participants must have relapsed after 1 or 2 prior lines of platinum-based chemotherapy. * Participants must have platinum-sensitive disease defined as radiographic progression greater than 183 days from the last dose of platinum-based chemotherapy. * Participants must have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 (assessed by the investigator) at baseline. Substudy 3 * Participants must be willing to provide an archival tumor tissue block or slides or must undergo a procedure to obtain a new tumor biopsy using a low-risk, medically routine procedure for immunohistochemistry (IHC) confirmation of FRα expression as defined by the central VENTANA FOLR1 (FOLR1-2.1) assay. Tumors must have FRα-expression in \>= 50% of viable tumor cells with \>= 2+ staining intensity. * Participants must have an Eastern Cooperative Oncology Group performance status of 0 or 1. * Participants must have a confirmed diagnosis of high-grade serous ovarian, primary peritoneal, or fallopian tube cancer. * Participants must have relapsed after 1 or 2 prior lines of platinum-based chemotherapy. * Participants must have platinum-sensitive disease defined as radiographic progression greater than 183 days from the last dose of platinum-based chemotherapy. * Participants must have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 (assessed by the investigator) at baseline. Exclusion Criteria: Substudy 1 * Participants with progressive disease (PD) while on triplet therapy or after the first day of their last triplet therapy cycle and before randomization. * Participants who receive an intervening dose of bevacizumab after the first day of their last triplet therapy cycle and before randomization. * Participants who received prior treatment with mirvetuximab soravtansine (MIRV), any FRα-targeting agent, or Poly(ADP-ribose) polymerase inhibitor (PARPi). Substudy 2 * More than 2 prior lines of chemotherapy. Lines of prior anticancer therapy are counted with the following considerations: * Neoadjuvant +/- adjuvant therapies are considered 1 line of therapy if the neoadjuvant and adjuvant correspond to 1 fully predefined regimen; otherwise, they are counted as 2 prior regimens. * Maintenance therapy (e.g., bevacizumab, PARPi) will be considered part of the preceding line of therapy (i.e., not counted independently). * If a chemotherapeutic agent in a regimen is substituted with another during a course of treatment due to toxicity, it will be considered part of the same line of therapy * Prior hormonal therapy will not be counted as a separate line of chemotherapy (it will be counted as part of the prior systemic therapy regimen) * Participants who received prior treatment with mirvetuximab soravtansine or other FRα-targeting agents. Substudy 3 * More than 2 prior lines of chemotherapy. Lines of prior anticancer therapy are counted with the following considerations: * Neoadjuvant +/- adjuvant therapies are considered 1 line of therapy if the neoadjuvant and adjuvant correspond to 1 fully predefined regimen; otherwise, they are counted as 2 prior regimens. * Maintenance therapy (e.g., bevacizumab, PARPi) will be considered part of the preceding line of therapy (i.e., not counted independently). * If a chemotherapeutic agent in a regimen is substituted with another during a course of treatment due to toxicity, it will be considered part of the same line of therapy * Prior hormonal therapy will not be counted as a separate line of chemotherapy (it will be counted as part of the prior systemic therapy regimen) * Participants who received prior treatment with mirvetuximab soravtansine or other FRα-targeting agents.