APL-2 and Pembrolizumab Versus APL-2, Pembrolizumab and Bevacizumab Versus Bevacizumab Alone for the Treatment of Recurrent Ovarian, Fallopian Tube, or Primary Peritoneal Cancer and Malignant Effusion

Inclusion Criteria: * Age \>= 18 years of age on day of signing informed consent * Recurrent epithelial ovarian/fallopian tube or primary peritoneal cancer (serous, clear cell, endometrioid, mixed or poorly differentiated or carcinosarcoma) based on imaging or synchronous primary ovarian and uterine cancer patients with any of the histology subtypes mentioned above regardless of platinum sensitivity, prior stage or number of prior treatment lines * Symptomatic ascites or pleural effusion or both requiring \>= 1 drainage within 4-weeks of study entry or has a peritoneal/pleural drainage catheter in place to control symptoms * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Patient has not received pembrolizumab or other immune checkpoint inhibitor treatment for 9 weeks prior to enrollment * Life expectancy of \>= 3 months * Absolute neutrophil count (ANC): \>= 1,500/µL * Platelets: \>= 75,000/µL * Hemoglobin: \>= 9 g/dL or 5.6 mmol/L (within 7 days of assessment) * Creatinine: =\< 1.5 X upper limit of normal (ULN) OR measured or calculated creatinine clearance \>= 60 mL/min (Cockcroft-Gault Equation) for participant with creatinine levels \> 1.5 X institutional ULN. GFR can also be used in place of creatinine or creatinine clearance (CrCl) * Total bilirubin: =\< 1.5 X ULN OR direct bilirubin =\< ULN for participants with total bilirubin levels \> 1.5 ULN * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\]) and alan…