A Study to Assess Adverse Events and Change in Disease Activity in Participants With Platinum-Resistant Advanced High-Grade Epithelial Ovarian, Primary Peritoneal, or Fallopian Tube Cancers With High Folate Receptor-Alpha Expression Treated With Intravenously (IV) Infused Mirvetuximab Soravtansine

Inclusion Criteria: Both Cohorts * Participants with a confirmed diagnosis of high-grade serous epithelial ovarian cancer (EOC), primary peritoneal cancer, or fallopian tube cancer. * Participants with platinum-resistant disease: * Participants with 1 prior line of platinum-based therapy who have received ≥ 4 cycles of platinum and had a response (complete response (CR) or partial response (PR)) followed by radiological progressive disease (PD) between > 3 months and ≤ 6 months after the date of the last dose of platinum. * Participants with 2 or 3 prior lines of platinum-based therapy who had radiological PD ≤ 6 months after the date of the last dose of platinum. * Participants with progression diagnosed radiographically on or after their most recent line of therapy. * Participants with an Eastern Cooperative Oncology Group Performance Status (ECOG PS) of 0 or 1.Performance status * Participants with ≥ 1 lesion that meets the definition of measurable disease by RECIST v1.1 (radiologically measured by the investigator). * Participants with a tumor that is positive for folate receptor alpha (FRα) expression as determined by the Ventana folate receptor 1 (FOLR1) assay (≥ 75% of tumor staining at 2+ intensity). Exclusion Criteria: Both Cohorts * Participants with endometrioid, clear cell, mucinous, or sarcomatous histology; mixed tumors containing any of the above histologies; or low-grade or borderline ovarian tumor. * Participants with primary platinum-refractory disease, defined as disease that did not respond (complete response (CR) or partial response (PR)) or that progressed radiographically within 3 months of the last dose of first-line platinum-containing chemotherapy. * Participants with serious concurrent illness or clinically relevant active infection as outlined in the protocol * Participants with a history of hemorrhagic or ischemic stroke within 6 months prior to randomization.