Inclusion Criteria: - Female participants with histologically-confirmed diagnosis of HGS ovarian, primary peritoneal, or fallopian tube cancer. - Platinum-resistant disease, defined as: - For participants who had only 1 line of platinum-based therapy: progression between > 1 month and ≤ 6 months after the last dose of platinum-based therapy of at least 4 cycles. - For participants who had 2 or 3 lines of platinum-based therapy: progression ≤ 6 months after the last dose of platinum-based therapy. - Participants have received at least 1 but no more than 3 prior lines of systemic therapy and for whom single-agent therapy is appropriate as the next line of therapy. Participants may have been treated with up to 1 line of therapy subsequent to determination of platinum-resistance. - Disease progression per RECIST v1.1 (by investigator assessment) of at least 1 measurable lesion on or after the most recent therapy. - Either formalin-fixed, paraffin-embedded (FFPE) tissue (up to 5 years old) or newly-obtained biopsies must be available for FRα assessment prior to randomization. - Eastern Cooperative Oncology Group Performance Status (ECOG PS) of 0 or 1. Exclusion Criteria: Medical Conditions - Clear cell, mucinous, endometrioid or sarcomatous histology, or mixed tumors containing components of any of these histologies, or low grade or borderline ovarian cancer. - Primary platinum-refractory ovarian cancer defined as disease progression within 1 month of the last dose of the first line platinum-containing regimen. - Pulmonary function test (PFT) abnormalities: FEV1 < 70% or FVC < 60%, and DLCO < 80%. - Investigator-assessed current ILD/pneumonitis, or ILD/pneumonitis suspected at screening or history of ILD/pneumonitis of any severity including ILD/pneumonitis from prior anti-cancer therapy. - Significant third-space fluid retention (eg, ascites or pleural effusion) that requires repeated drainage. Physical and Laboratory Test Findings - Evidence of organ dysfunction or any clinically-significant deviation from normal in physical examination, vital signs, ECG, or clinical laboratory determinations beyond what is consistent with the target population. Allergies and Adverse Drug Reactions - Has any prior severe hypersensitivity (≥ Grade 3) to monoclonal antibodies or eribulin or contraindication to the receipt of corticosteroids or any of the excipients (investigators should refer to the prescribing information for the selected corticosteroid). - History of allergy or contraindication to IC chemotherapy agent selected if randomized to Arm C. Other protocol-defined inclusion/exclusion criteria apply.