Pembrolizumab Combined With Bevacizumab With or Without Agonist Anti-CD40 CDX-1140 for the Treatment of Patients With Recurrent Ovarian Cancer

Inclusion Criteria: * Age \>= 18 years of age. * Recurrent serous (low grade or high grade), endometrioid, or clear cell recurrent epithelial ovarian, fallopian tube, or primary peritoneal cancer. * Participant can be either platinum-sensitive or platinum-resistant, no more than 4 prior lines of treatment, and BRCA status must be known. Neoadjuvant + adjuvant is considered one line. * Participants may have received a prior PARPi, this will not be considered a separate line of therapy if received in maintenance. * Participants may have received a prior anti-PD1/anti-PDL1 therapy or bevacizumab, these will not be considered a separate line of therapy. * Any chemotherapy regimen change due to toxicity in the absence of disease progression will be considered part of the same line of therapy. * Hormonal therapy for OC (e.g. Tamoxifen, aromatase inhibitors etc.) will not count as a separate line of prior therapy. * Anticipated lifespan greater than 6 months. * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Patient has measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria present. * All residual toxicity related to prior anti-cancer therapies (excluding alopecia, grade 2 fatigue, vitiligo, endocrinopathies on stable replacement therapy, grade 2 neuropathy from taxanes or platinum and grade 2 hearing loss from platinum) must be resolved to grade 1 severity or less (or returned to baseline) prior to receipt of study treatment. * Absolute neutrophil count (ANC): \>= 1,500 /mcL. * Platelets: \>= 100,000 / mcL. * Hemoglobin: \>= 8 g/dL or 5.0 mmol/L transfusion allowed with adequate bone marrow function * Creatinine clearance \>= 50 mL/min. * Total bilirubin: =\< 2 X upper limit of normal (ULN) except patients with Gilbert's syndrome or liver involvement, who must have a total bilirubin =\< 3 mg/dL. * Aspartate aminotransferase (AST) ( serum glutamic-oxaloacetic transaminase \[SGOT\] ) and alanine aminotransferase (ALT) ( serum glutamate pyruvate transaminase \[SGPT\]): =\< 2.5 X ULN OR =\< 5 X ULN for participants with liver metastases. * Albumin: \> 2.5 mg/dL. * International normalized ratio (INR) OR prothrombin time (PT) activated partial thromboplastin time (APTT) =\< 1.5 x ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants. * Participant must be willing to undergo core or excisional biopsy of a tumor lesion within 7 days prior to the first dose of investigational product and after 3 cycles of treatment(prior to cycle 4-day 1: mandatory only if available) and, at the end of treatment (optional). Participants for whom newly obtained samples cannot be provided at baseline (e.g., inaccessible or subject safety concern), may submit an archived specimen, only upon agreement from the Prinicipal Investigator, if available). * A woman of childbearing potential must have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Participants of childbearing potential must be willing to use 2 methods of birth control or be surgically sterile or abstain from heterosexual activity for the course of the study through 6 months after the last dose of study medication (participants of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year). Should a woman become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately. * Participant (or legal representative) must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure. Exclusion Criteria: * Primary platinum-refractory patients are excluded * Has a nonepithelial cancer (germ cell tumors, sex cord-stromal tumors), borderline tumors, mucinous or seromucinous that is predominately mucinous, malignant Brenner's tumor, carcinosarcoma or undifferentiated carcinoma. * Receipt of any antibody targeting T cell checkpoint or co-stimulation pathways within 4 weeks, use of any other monoclonal based therapies within 4 weeks, and all other immunotherapy (tumor vaccine, cytokine, or growth factor given to control the cancer) within 2 weeks prior to the planned start of study treatment. * Has received prior systemic anticancer therapy (including investigational agents or maintenance therapy) within 28 days prior to the planned start of study treatment. Hormonal therapy is allowed until the time of randomization * Progression on prior immune checkpoint blockade therapy. * Systemic radiation therapy within 4 weeks, prior focal radiotherapy within 2 weeks prior to the first dose of study treatment. * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug * Major surgery within 4 weeks prior to the first dose of study treatment. Surgery requiring local/epidural anesthesia must be completed at least 72 hours before study drug administration and patients should be recovered. * Known or prior malignancy requiring active treatment in the past 2 years. Exception: basal or squamous cell skin cancer or in situ cancers; or any other cancer from which the patient has been disease-free for at least 3 years. * Active, untreated central nervous system metastases. Patients with brain metastases identified at screening may be rescreened after the lesion(s) have been appropriately treated; patients with treated brain metastases should be neurologically stable for 4 weeks post-treatment and prior to study enrollment, and off corticosteroids for at least 2 weeks before administration of study drugs, and treated lesions should demonstrate no new growth on the re-screening scan. * History of (non-infectious) pneumonitis or has current pneumonitis, including grade 1 (asymptomatic; clinical or diagnostic observations only; intervention not indicated) pneumonitis. * History of severe hypersensitivity reactions to other monoclonal antibodies (mAbs). * Prior therapy with any anti-CD40 antibody. * Hypersensitivity to bevacizumab, pembrolizumab, or any of its excipients. * Has active autoimmune disease that has required systemic treatment in the past 2 years except replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid) * Known active or chronic viral hepatitis or history of any type of hepatitis within the last 6 months. * Has an acute infection requiring systemic therapy * Known immunodeficiency or active human immunodeficiency virus (HIV) * Concurrent active Hepatitis B (defined as HBsAg positive and/or detectable HBV DNA)and Hepatitis C virus (defined as anti-HCV Ab positive and detectable HCV RNA) infection. Note: Hepatitis B and C screening tests are not required unless known history of HBV and HCV infection * Has an active infection requiring systemic therapy * Known immunodeficiency or active HIV * Has received any investigational vaccines (i.e., those not licensed or approved for emergency use). Note: Any licensed COVID-19 vaccine (including for Emergency Use) is allowed in the study as long as they are mRNA vaccines, adenoviral vaccines, or inactivated vaccines. These vaccines will be treated just as any other concomitant therapy. Investigational vaccines (i.e., those not licensed or approved for Emergency Use) are not allowed. * Mental impairment that may compromise the ability to give informed consent and comply with the requirements of the study. * Subject requires or is likely to require more than a two-week course of corticosteroids for intercurrent illness. Subject must complete the course of corticosteroids 2 weeks before screening to meet eligibility. * Subject has a serious, non-healing wound, ulcer, or bone fracture. * Subject has a clinically significant cardiovascular disease including: * Uncontrolled hypertension \< 150/90 mmHg (may be rescreened after adequate control) * Myocardial infarction or unstable angina within 6 months prior to enrollment * New York Heart Association (NYHA) Grade II or greater congestive heart failure. * New onset on thromboembolic event or hemorrhage within 6 weeks prior to randomization * Subject has organ allografts. * Subject has clinical symptoms or signs of partial or complete gastrointestinal obstruction or require parenteral hydration and/or nutrition. * Pregnant or nursing female participants. * Known active alcohol or drug abuse. * Unwilling or unable to follow protocol requirements. * Any condition which in the investigator's opinion deems the participant an unsuitable candidate to receive study drug.