A Phase II Study Of Nivolumab/ Bevacizumab/Rucaparib

Inclusion Criteria: * Participants must have histologic or cytologic confirmation of epithelial ovarian cancer, fallopian tube or peritoneal cancer. All histologies (including serous, mucinous, endometrioid, clear cell, MMMTs, and mixed histologies) are eligible. All tumor grades are eligible. * Participants must have received a first-line platinum-based chemotherapy regimen * Participants must have relapsed disease despite standard therapy. * For Cohorts 1 and 2: Participants with platinum-resistant or platinum-sensitive disease (within 12 months) are eligible. Platinum-resistant disease is defined as relapse within 6 months after the last dose of platinum-based chemotherapy. Platinum-sensitive disease is defined as relapse greater than 6 months after the last dose of platinum-based chemotherapy. Participants with platinum-sensitive disease who have experienced relapse within 6 to 12 months after the last dose of platinum-based chemotherapy are eligible.Participants with primary platinum-refractory disease (defined as progression during or relapsed within 2 months of their initial platinum-based chemotherapy) are not eligible. For Cohort 3: Participants must have platinum-sensitive disease and have experienced relapse within 6 to 12 months (i.e., 180 to 365 days) after the last dose of platinum-based chemotherapy. * Participants must have received no more than 3 prior chemotherapy regimens. There is no limit to the number of prior hormonal therapies. * Participants must have measurable disease by RECIST 1.1 criteria. * Participants who have received prior bevacizumab are eligible unless there is evidence of unacceptable toxicity due to prior bevacizumab exposure. * Participants may not have received any prior treatment with an anti-PD-1, anti PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or immune checkpoint pathways. * Participants must have stopped any hormonal therapy at least 1 week prior to treatment with nivolumab and bevacizumab.Participants may continue on hormone replacement therapy administered for post-menopausal symptoms. * Age ≥ 18 years * Estimated life expectancy of greater than 6 months. * ECOG performance status of 0 or 1 * Screening laboratory values must meet the following criteria and should be obtained within 14 days prior to registration: * WBC ≥ 2,000/µL * Neutrophils ≥ 1,500/µL * Platelets ≥ 100,000/mcL * Hemoglobin \> 9.0 g/dL * Serum creatinine within the institutional ULN or creatinine clearance (CrCl) ≥ 60 mL/min (calculated using the Cockgroft-Gault formula) for participants with serum creatinine levels above institutional ULN * AST (SGOT) / ALT (SGPT) ≤ 3 × institutional ULN * Total bilirubin ≤ 1.5 × institutional ULN (except participants with Gilbert Syndrome, who can have total bilirubin ≤ 3.0 × institutional ULN with direct bilirubin that is within institutional ULN) * Coagulation parameters (INR, aPTT) ≤ 1.25 × institutional ULN * Patients with treated limited stage basal cell or squamous cell carcinoma of the skin or carcinoma in situ of the breast or cervix are eligible. Patients with stage IA endometrial cancer are eligible if the following conditions are met: without vascular or lymphatic invasion AND no serous, clear cell or grade 3 histology. Patients with early stage I or II cancers treated with curative intent who have no evidence of recurrent cancer 3 years following diagnosis and judged by the investigator to be at low risk of recurrence are eligible. * Participants must have biopsiable disease and be willing to undergo pre-treatment biopsy, or have an archival tumor sample obtained \< 20 months prior to study entry. * Women of childbearing potential (WOCBP) is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal. Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes. Additionally, women under the age of 62 who are not surgically sterile must have a documented serum follicle stimulating hormone (FSH) level less than 40 mIU/mL to document postmenopausal status. * Nivolumab, bevacizumab, and rucaparib may each cause fetal harm or risk to human pregnancy. For this reason, WOCBP must agree to use appropriate method(s) of contraception for 6 months after the last dose of study treatment, per FDA recommendations on use of contraception following bevacizumab. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. Patients receiving rucaparib should immediately discontinue rucaparib if they should become pregnant or suspect they are pregnant. * WOCBP must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of study treatments. * Women must not be breastfeeding * Participants are permitted to use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic absorption). Physiologic replacement doses of systemic corticosteroids are permitted, even if \> 10 mg/day prednisone equivalents, in the absence of active autoimmune disease. A brief course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction caused by contact allergen) is permitted. * Ability to understand and the willingness to sign a written informed consent document. Specific criteria for Cohort 2 and 3 -Patients must have undergone germline BRCA testing and must not have a deleterious or suspected deleterious BRCA mutation. Where tumor testing has been performed, patients with a deleterious or suspected deleterious somatic BRCA mutation are also not eligible. Exclusion Criteria: * Patients with platinum-refractory disease are ineligible. Platinum-refractory disease is defined as relapse less than 2 months after the last dose of platinum-based chemotherapy. * Patients with platinum-sensitive disease with relapse greater than 12 months after the last dose of platinum-based chemotherapy are ineligible. * Participants who have had chemotherapy or radiotherapy within 3 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 3 weeks earlier. * Participants may not be receiving any other investigational agents nor have participated in an investigational trial within the past 4 weeks. * Participants must agree not to use natural herbal products or other "folk remedies" while participating in this study. * Patients with a history of allergic reactions attributed to bevacizumab or to compounds of similar chemical or biologic composition to nivolumab or bevacizumab are excluded. * Patients are excluded if they have active brain metastases or leptomeningeal metastases. Subjects with brain metastases are eligible if metastases have been treated and there is no magnetic resonance imaging (MRI) evidence of progression for at least 6 months after treatment is complete and within 28 days prior to the first dose of nivolumab and bevacizumab administration. There must also be no requirement for immunosuppressive doses of systemic corticosteroids (\> 10 mg/day prednisone equivalents) for at least 2 weeks prior to study drug administration. * Patients with any of the following cardiovascular diseases are excluded: * History of myocardial infarction within six months * Unstable angina * Angina pectoris that requires the use of anti-anginal medication * History of documented congestive heart failure (NYHA classification of III or IV) or documented cardiomyopathy * Valvular disease with documented compromise in cardiac function * If cardiac function assessment is clinically indicated or performed: LVEF less than normal per institutional guidelines, or \< 55%, if threshold for normal not otherwise specified by institutional guidelines * Any prior history of hypertensive crisis or hypertensive encephalopathy * Patients may not have any evidence of pre-existing inadequately controlled hypertension (defined as a systolic BP of \>140 mmHg or a diastolic BP of \>90 mmHg), and must have a normal blood pressure (≤140/90 mmHg) taken in the clinic setting by a medical professional within 2 weeks prior to starting study. * Clinically significant peripheral vascular disease * Vascular disease including aortic aneurysm or dissection * History of stroke, transient ischemic attack or subarachnoid hemorrhage * Ventricular arrhythmias except for benign premature ventricular contractions * Cardiac conduction abnormality requiring a pacemaker * Known history of QT/QTc prolongation or torsades de pointes * QTc prolongation \> 470 msec or other significant ECG abnormality noted during screening * Grade 2 or higher proteinuria (2+ or higher protein on urinalysis or urine protein:creatinine (UPC) ratio ≥ 1.0; if both tests are performed, UPC should be used to evaluate eligibility) or hematuria. * Participants may not have evidence of a bowel obstruction, abdominal fistula, or intra-abdominal abscess within 6 months of study entry. Participants with current signs or symptoms suggestive of bowel obstruction including early or partial obstruction are ineligible. Participants with a history of gastrointestinal perforation at any time point are ineligible. * Non-healing wound, ulcer or bone fracture. * Serious active infection requiring intravenous antibiotics and/or hospitalization at study entry. * Current dependency on IV hydration or TPN. * Any patient with a history of major depressive episode, bipolar disorder, obsessive/compulsive disorder, schizophrenia, a history of suicide attempt or ideation, or homicide/homicidal ideation as judged by the investigator and/or based on recent psychiatric assessment may not participate in this study without discussion with and agreement of the study PI. * Uncontrolled current illness including, but not limited to, ongoing or active infection or psychiatric illness/social situations that would limit compliance with study requirements. * Patients are excluded if they have an active, known or suspected autoimmune disease other than the following: vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger. * Patients are excluded if they have a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration, with the exception of a brief course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction caused by contact allergen). Participants are permitted to use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic absorption). * Patients are excluded if they test positive for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV antibody) indicating acute or chronic infection. * Patients are excluded if they have known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS). * Evidence of prior or current coagulopathy or bleeding diathesis. * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to starting nivolumab and bevacizumab * History of severe infusion reactions to monoclonal antibody therapy Specific criteria for Cohort 2 and 3 * Patients who have received a prior PARP inhibitor are not allowed to enroll to Cohort 2 of the trial * Patients are excluded from Cohort 2 or Cohort 3 should they have pre-existing duodenal stent and/or any gastrointestinal disorder or defect that would, in the opinion of the investigator, interfere with absorption of rucaparib.