Sacituzumab Govitecan With Bevacizumab Compared to Usual Chemotherapy (Carboplatin, Pegylated Liposomal Doxorubicin and Bevacizumab) for Treating Recurrent Platinum-Sensitive Ovarian Cancer After PARP Inhibitor Maintenance Therapy

Inclusion Criteria: * Patients must have histologic diagnosis of high grade serous or endometrioid epithelial ovarian cancer * Ovarian cancer = fallopian tube, ovarian, and primary peritoneal cancer * Disease must be platinum sensitive, as defined by progression documented ≥ 6 months (182 days) from the last receipt of platinum * Disease must have progressed during first line maintenance PARP inhibitor (PARPi) for advanced ovarian cancer. NO intervening therapies between progression on PARPi and study registration are permitted * Disease must be germline or somatic BRCA1 or BRCA2 mutated or homologous recombination deficiency test positive * Disease must be measurable or non-measurable as defined by Response Evaluation Criteria in Solid Tumors (RECIST) version (v.) 1.1 * Secondary or cytoreductive surgery, after start of treatment on this trial, and prior to documentation of disease progression, is NOT permitted * No previous receipt of any topoisomerase-I inhibiting agents * No investigational agents within 4 weeks of study registration * No current treatment with any other (non-study) cytotoxic chemotherapy, targeted therapy, biologic therapy, immunotherapy or endocrine therapy for the treatment of the disease under the current study * Last dose of PARP inhibitor treatment must be ≥ 3 weeks before study registration * Patients with treated brain metastases are eligible if follow-up brain imaging 4 weeks after CNS-directed therapy shows no evidence of disease progression. Patients with brain metastases must have follow up imaging demonstrating no evidence of disease progression and that the disease is stable off of steroids * Age ≥ 18 * Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2 * Not pregnant and not nursing * Absolute neutrophil count (ANC) ≥ 1,500 cells/mm\^3 * Platelets ≥ 100,000 cells/mm\^3 * Hemoglobin ≥ 9 g/dl (Note: The use of transfusion or other intervention to achieve hemoglobin \[Hgb\] ≥ 9 g/dl is acceptable) * Creatinine clearance (CrCL) of ≥ 30 mL/min by the Cockcroft-Gault formula * Urinalysis with ≤ 1+ protein and/or urine protein \< 1.0 g/24 hours (hrs) * Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) (patients with known Gilbert's disease who have bilirubin level ≤ 3 x institutional ULN may be enrolled) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3 x institutional ULN * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association functional classification. To be eligible for this trial, patients should be class 2B or better * No active infection requiring parenteral antibiotics * No non-healing wound, ulcer, or bone fracture * No current evidence of intra-abdominal abscess, abdominal/pelvic fistula (not diverted), gastrointestinal perforation, gastrointestinal (GI) obstruction, and/or need for drainage nasogastric or gastrostomy tube * No clinically significant bleeding within 28 days prior to registration * No uncontrolled hypertension, defined as systolic ≥ 160 mm Hg or diastolic ≥ 100 mm Hg * Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) with the following exceptions: * Patients with grade 2 or lower neuropathy, any grade alopecia, well controlled hypertension, thyroid disease controlled with therapy, and history of thromboembolic disease on anticoagulation are eligible * Patients with laboratory-based grade 2 or higher adverse events (AEs) that meet the criteria outlined above are eligible * No major surgery within 3 weeks prior to study registration * Patients who underwent major surgery must have recovered adequately from any toxicity and/or complications from surgery prior to study registration * No strong inhibitors or inducers of UGT1A1 * No history of allergic reaction to the study agent(s), compounds of similar chemical or biologic composition to the study agent(s) (or any of its excipients)