A Study of Mirvetuximab Soravtansine vs. Investigator's Choice (IC) of Chemotherapy in Platinum-Resistant, Advanced High-Grade Epithelial Ovarian, Primary Peritoneal, or Fallopian Tube Cancers With High Folate Receptor-Alpha (FRα) Expression

Inclusion Criteria: 1. Female participants ≥ 18 years of age 2. Participants must have a confirmed diagnosis of high-grade serious epithelial ovarian cancer, primary peritoneal cancer, or fallopian tube cancer 3. Participants must have platinum-resistant disease: 1. Participants who have only had 1 line of platinum based therapy must have received at least 4 cycles of platinum, must have had a response (CR or PR) and then progressed between \>3 months and ≤ 6 months after the date of the last dose of platinum 2. Participants who have received 2 or 3 lines of platinum therapy must have progressed on or within 6 months after the date of the last dose of platinum 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. Note: Participants who are platinum-refractory during front-line treatment are excluded 4. Participants must have progressed radiographically on or after their most recent line of therapy 5. Participants must be willing to provide an archival tumor tissue block or slides, or undergo procedure to obtain a new biopsy using a low risk, medically routine procedure for immunohistochemistry (IHC) confirmation of FRα positivity 6. Participant's tumor must be positive for FRα expression as defined by the Ventana FOLR1 (FOLR-2.1) CDx assay 7. Participants must have at least one lesion that meets the definition of measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) Version 1.1 (radiologically measured by the Investigator) 8. Participants must have received at least 1 but no more than 3 prior systemic lines of anticancer therapy, and for whom single-agent therapy is appropriate as the next line of treatment: 1. Adjuvant ± neoadjuvant considered one line of therapy 2. Maintenance therapy (for example, bevacizumab, poly (ADP-ribose) polymerase \[PARP\] inhibitors) will be considered as part of the preceding line of therapy (that is, not counted independently) 3. Therapy changed due to toxicity in the absence of progression will be considered as part of the same line (that is, not counted independently) 4. Hormonal therapy will be counted as a separate line of therapy unless it was given as maintenance 9. Participant must have an Eastern Cooperative Oncology Group Performance Status (ECOG PS) of 0 or 1 10. Time from prior therapy: 1. Systemic antineoplastic therapy (5 half-lives or 4 weeks, whichever is shorter) 2. Focal radiation completed at least 2 weeks prior to first dose of study drug 11. Participants must have stabilized or recovered (Grade 1 or baseline) from all prior therapy-related toxicities 12. Major surgery must be completed at least 4 weeks prior to first dose and have recovered or stabilized from the side effects of prior surgery 13. Participants must have adequate hematologic, liver and kidney functions defined as: 1. Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/liter (L) (1,500/microliter \[μL\]) without granulocyte colony-stimulating factor (G-CSF) in the prior 10 days or long-acting white blood cell (WBC) growth factors in the prior 20 days 2. Platelet count ≥ 100 x 10\^9/L (100,000/μL) without platelet transfusion in the prior 10 days 3. Hemoglobin ≥ 9.0 g/dL without packed red blood cell (PRBC) transfusion in the prior 21 days 4. Serum creatinine ≤ 1.5 x upper limit of normal (ULN) 5. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3.0 x ULN 6. Serum bilirubin ≤ 1.5 x ULN (participants with documented diagnosis of Gilbert syndrome are eligible if total bilirubin \< 3.0 x ULN 7. Serum albumin ≥ 2 grams (g)/deciliter (dL) 14. Participants or their legally authorized representative must be willing and able to sign the informed consent form (ICF) and to adhere to the protocol requirements 15. Women of childbearing potential (WCBP) must agree to use highly effective contraceptive method(s) while on study drug and for at least 3 months after the last dose of MIRV or at least 6 months after the last dose of paclitaxel, pegylated liposomal doxorubicin, or topotecan 16. WCBP must have a negative pregnancy test within 4 days prior to the first dose of study drug Exclusion Criteria: 1. Participants with endometrioid, clear cell, mucinous, or sarcomatous histology, mixed tumors containing any of the above histologies, or low-grade or borderline ovarian tumor 2. Participants with primary platinum-refractory disease, defined as disease that did not respond to (CR or PR) or has progressed within 3 months of the last dose of first line platinum-containing chemotherapy 3. Participants with prior wide-field radiotherapy (RT) affecting at least 20% of the bone marrow 4. Participants with \> Grade 1 peripheral neuropathy per Common Terminology Criteria for Adverse Events (CTCAE) v5.0 5. Participants with active or chronic corneal disorders, history of corneal transplantation, or active ocular conditions requiring ongoing treatment/monitoring such as uncontrolled glaucoma, wet age-related macular degeneration requiring intravitreal injections, active diabetic retinopathy with macular edema, macular degeneration, presence of papilledema, and /or monocular vision 6. Participants with serious concurrent illness or clinically relevant active infection, including, but not limited to the following: 1. Active hepatitis B or C infection (whether or not on active antiviral therapy) 2. Human immunodeficiency virus (HIV) infection 3. Active cytomegalovirus infection 4. Any other concurrent infectious disease requiring IV antibiotics within 2 weeks before starting study drug Note: Testing at screening is not required for the above infections unless clinically indicated 7. Participants with history of multiple sclerosis or other demyelinating disease and/or Lambert-Eaton syndrome (paraneoplastic syndrome) 8. Participants with clinically significant cardiac disease including, but not limited to, any one of the following: 1. Myocardial infarction ≤ 6 months prior to first dose 2. Unstable angina pectoris 3. Uncontrolled congestive heart failure (New York Heart Association \> class II) 4. Uncontrolled ≥ Grade 3 hypertension (per CTCAE) 5. Uncontrolled cardiac arrhythmias 9. Participants assigned to PLD stratum only: Left ventricular ejection fraction (LVEF) below the institutional limit of normal as measured by echocardiography (ECHO) or multigated acquisition (MUGA) scan 10. Participants with a history of hemorrhagic or ischemic stroke within six months prior to randomization 11. Participants with a history of cirrhotic liver disease (Child-Pugh Class B or C) 12. Participants with a previous clinical diagnosis of non-infectious interstitial lung disease (ILD), including noninfectious pneumonitis 13. Participants with required use of folate-containing supplements (for example, folate deficiency) 14. Participants with prior hypersensitivity to monoclonal antibodies 15. Women who are pregnant or lactating 16. Participants with prior treatment with MIRV or other FRα-targeting agents 17. Participants with untreated or symptomatic central nervous system (CNS) metastases 18. Participants with a history of other malignancy within 3 years prior to randomization. Note: does not include tumors with a negligible risk for metastasis or death (for example, adequately controlled basal-cell carcinoma or squamous-cell carcinoma of the skin, or carcinoma in situ of the cervix or breast 19. Prior known hypersensitivity reactions to study drugs and/or any of their excipients 20. People who are detained through a court or administrative decision, receiving psychiatric care against their will, adults who are the subject of a legal protection order (under tutorship/curatorship), people who are unable to express their consent, and people who are subject to a legal guardianship order 21. Simultaneous participation in another research study, in countries or localities where this is the health authority guidance