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

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.