This is a single-institution, single-arm study with a safety lead-in to determine if previously established safe doses of autophagy drugs, hydroxychloroquine (HCQ) and nelfinavir mesylate (NFV) will benefit ovarian cancer patients in a maintenance setting. Patients will receive the two study drugs HCQ and NFV in combination with maintenance bevacizumab.

Inclusion Criteria:

• Participants must have platinum-sensitive first recurrent high-grade serous or high-grade predominantly serous ovarian cancer, fallopian tube cancer, or primary peritoneal cancer. Patients must have had a 6-month disease-free progression since last platinum chemotherapy to be considered platinum sensitive.
• All participants must agree to have previously undergone genetic testing with germline panel testing with at least BRCA 1/2 mutation status known and/or somatic tumor next generation sequencing with homologous recombination deficiency (HRD) testing and/or loss of heterozygosity (LOH) known.
• Participants must be enrolled within 3-8 weeks of the first day of the last cycle of platinum-based chemotherapy for their first cancer recurrence. - Participants must have received at least 3-courses of bevacizumab during chemotherapy and have a plan to continue maintenance bevacizumab therapy.
• Evidence of platinum-sensitive response to current platinum-based chemotherapy with a partial or complete response based on imaging or CA-125 trend
• Participants of childbearing potential must have a negative serum or urine pregnancy test (beta human chorionic gonadotropin [hCG]) within 7 days before receiving the first dose of study treatment.
• Voluntary, signed, and dated, Institutional Review Board (IRB) approved consent form per regulatory and institutional guidelines.
• 18 years of age or older.
• ECOG performance status of 0-2
• Bilirubin ≤ 1.5 times the upper limit of normal (ULN) and AST / ALT ≤ 3 times ULN. Subjects with Gilbert's syndrome may be included if the total bilirubin is < 3 times ULN and the direct bilirubin is within normal limits.
• CrCl ≥35 mL/min, according to the Cockgroft-Gault formula.
• Absolute neutrophil count (ANC) ≥ 1,000 cells/mm3.
• Platelet count ≥ 75,000 cells / mm3
• Hemoglobin ≥ 9 g/ dL, recent transfusion is allowed, though must be ≥ 7 days C1D1 of investigational agents
• Adequately controlled blood pressure (<160 mm Hg/100 mm Hg) as determined by the treating investigator.
• Subjects with the potential to produce children must agree to effective contraceptive method use during study participation and at least 6 months after discontinuation of the study.
• Patients requiring narcotic analgesics must be on stable doses for at least 2 weeks before study entry.
• Patients must discontinue any statin use within 48 hours of beginning study treatment.
• Patients must have a QT interval of <450 ms on screening upon ECG.
• Patients who have diabetes mellitus must have it well-controlled (A1c of <8%).

Exclusion Criteria:

• New York Heart Association (NYHA) Class III or IV cardiac disease, myocardial infarction within the past 6 months, unstable arrhythmia, or history of ischemia on baseline ECG.
• Underlying psychiatric disorder requiring hospitalization within the last two years.
• Clinically significant neurological disorder (Parkinson's disease, dementia, multiple sclerosis), as determined by the enrolling investigator.
• Platinum resistant or refractory disease
• Active, uncontrolled bacterial, viral, or fungal infection, requiring systemic therapy.
• Treatment with local or systemic radiation therapy, surgery, or investigational therapy within 28 days before registration with the exception of the platinum doublet and bevacizumab.
• Unwillingness or inability to comply with procedures required in this protocol.
• Serious nonmalignant disease that could compromise protocol objectives in the opinion of the Investigator.
• Patients who are receiving coumadin
• Patients who are currently participating in any other clinical trial of an investigational product.
• Any other mental incapacitation or psychiatric illness that would preclude study participation, as determined by the enrolling investigator.
• Prisoners or patients who are compulsorily detained (involuntarily incarcerated) for treatment of either a psychiatric or physical (e.g., infectious disease) illness must not be enrolled in this study.
• Female patients who are of child-bearing potential (WOCBP) who are pregnant or planning to become pregnant during the study or within 6 months of the last dose of study drugs. A urine pregnancy test for WOCBP will be collected during the screening period. Females will be determined not to be of child-bearing potential with a history of hysterectomy, tubal ligation, dual salpingo-oophorectomy, or age 45 or older with postmenopausal status > 12 months.
• Patients unable to stop taking strong inhibitors and inducers of CYP2C8, CYP3A4, CYP2C19, CYP2D6, FMO-1, and MAO-A.
• Patients unable to stop taking substrates of CYP2D6, CYP3A4, P-gp, MATE1K, and MATE2K.
• Patients diagnosed with myasthenia gravis
• Patients with G6PD Deficiency
• Patients with porphyria
• Platinum-sensitive patients that are candidates for PARP inhibitor maintenance, patients will be allowed if previously did not tolerate PARP and opt against PARP maintenance
• Patients that have contraindications to bevacizumab, as per approved product labeling
• Patients that have a high ASCVD score based on the American College of Cardiology ASCVD Risk Estimator Plus calculator and who should not stop their statin due to cardiovascular risk