Inclusion Criteria:  Patients must have histologically confirmed metastatic or recurrent solid tumor malignancy for which standard curative or palliative measures do not exist or are no longer effective  Dose escalation/phase I: Metastatic or recurrent solid tumors with measurable or evaluable disease Dose expansion exploratory cohorts (nivolumab + ipilimumab + ZEN003694): Recurrent BRCAwt epithelial ovarian carcinoma patients who have progressed or recurred within <6 months from prior platinum-based therapy Dose expansion exploratory cohorts: Patients must have measurable and biopsiable disease (at least two lesions) per Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 No more than 5 lines of prior therapy for the dose escalation and expansion phases In the expansion cohorts, up to 2 prior lines in the platinum-resistant setting is allowed Patients with primary refractory ovarian cancer (who progressed while on primary 1L platinum therapy) will be excluded in the dose expansion cohorts but allowed in the dose escalation cohort  Patients who have had chemotherapy or radiotherapy more than 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study and who have recovered from adverse events due to agents administered more than 4 weeks earlier are eligible. Prior palliative (limited field) radiation therapy is permitted, if all of the following criteria are met:  Palliative radiation must have been completed at least 4 weeks before starting study treatment Repeat imaging demonstrates no new sites of bone metastases Irradiated sites of metastasis should not ae selected as target lesions Patients must have recovered to meet all eligibility criteria Age >= 18 years. Because no dosing or AE data are currently available on the use of nivolumab in combination with ZEN003694 +/- ipilimumab in patients < 18 years of age, children are excluded from this study Eastern Cooperative Oncology Group (ECOG) performance status =< 1 (Karnofsky >= 80%) Leukocytes >= 2,000/mcL Absolute neutrophil count >= 1,500/mcL Platelets >= 150,000/mcL Total bilirubin =<1.5 x institutional upper limit of normal (ULN) Aspartate aminotransferase (AST)(serum glutamic-oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT)(serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x institutional ULN Creatinine clearance (CrCl) >= 60 mL/min (using the Chronic Kidney Disease Epidemiology Collaboration [CKD-EPI] formula) Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial 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 and have a corrected QT (QTc) interval < 450 msec  The effects of nivolumab, ZEN003694, and/or ipilimumab on the developing human fetus are unknown. For this reason and because nivolumab, ZEN003694, and/or ipilimumab are known to be teratogenic, women of child-bearing potential (WOCBP) and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. WOCBP should use an adequate method to avoid pregnancy for 5 months after the last dose of investigational drug. Women of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin [HCG]) within 24 hours prior to the start of nivolumab. Women must not be breastfeeding. Men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1% per year. Women who are not of childbearing potential (i.e., who are postmenopausal or surgically sterile as well as azoospermic men) do not require contraception.  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. In addition, women under the age of 55 must have a documented serum follicle stimulating hormone (FSH) level less than 40 mIU/mL. WOCBP receiving nivolumab will be instructed to adhere to contraception for a period of 5 months after the last dose of investigational product. These durations have been calculated using the upper limit of the half-life for nivolumab (25 days) and are based on the protocol requirement that WOCBP use contraception for 5 half-lives plus 30 days and men who are sexually active with WOCBP use contraception for 5 half-lives plus 90 days. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she (or the participating partner) should inform the treating physician immediately Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity (IDMC) who have a legally-authorized representative (LAR) and/or family member available will also be eligible  Exclusion Criteria:  Patients with sarcoma or non-epithelial histology Patients with known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e., without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to the first dose of study intervention Prior therapy with PD-1, PD-L1, or CTLA-4 inhibitors, or any other antibody or drug specifically targeting T-cell co-stimulation or immune checkpoint pathways. Prior anti-PD-1/PD-L1 in microsatellite instability-high (MSI-H) tumors is allowed in the dose escalation cohort if no grade 2 or more toxicities developed during that therapy requiring stopping immune checkpoint inhibition. Patients who have received prior vaccine therapy are eligible History of allergic reactions attributed to compounds of similar chemical or biologic composition to nivolumab, ipilimumab, and/or ZEN003694, including severe hypersensitivity reactions to any monoclonal antibody Patients who are receiving any other investigational agents  Patients with human immunodeficiency virus (HIV) infection may be enrolled on this study provided: (a) they are on a stable regimen of highly active anti-retroviral therapy (HAART) with no medications otherwise prohibited by this protocol (e.g. drug-drug interactions,), e.g. medications cannot be CYP3A4 inducers or inhibitors and cannot interact with ZEN003694), and (b) they require no concurrent antibiotics or antifungals for the prevention of opportunistic infections, and (c) they have a CD4 count above 250 cell/mcL and an undetectable viral load on standard polymerase chain reaction (PCR)-based tests within 1 month of initiation of study treatment.  Other patients with clinically significant immunosuppression, e.g. organ transplant patients, are not eligible. If clarification is needed, this may be discussed with the medical monitor. Patients should be excluded if they have a positive test for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV RNA) indicating acute or chronic infection Patients with active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including systemic corticosteroids, should be excluded. These include but are not limited to patients with a history of immune related neurologic disease, multiple sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, myasthenia gravis; systemic autoimmune disease such as systemic lupus erythematosus (SLE), connective tissue diseases, scleroderma, inflammatory bowel disease (IBD), Crohn's, ulcerative colitis, hepatitis; and patients with a history of toxic epidermal necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome should be excluded because of the risk of recurrence or exacerbation of disease. Patients with vitiligo, endocrine deficiencies including thyroiditis managed with replacement hormones including physiologic corticosteroids are eligible. Patients with rheumatoid arthritis and other arthropathies, Sjogren's syndrome and psoriasis controlled with topical medication and patients with positive serology, such as antinuclear antibodies (ANA), anti-thyroid antibodies should be evaluated for the presence of target organ involvement and potential need for systemic treatment but should otherwise be eligible Patients should be 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. Inhaled or topical steroids and adrenal replacement doses < 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. Patients 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. 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 Patients who have had evidence of active or acute diverticulitis, intra-abdominal abscess, gastrointestinal (GI) obstruction and abdominal carcinomatosis which are known risk factors for bowel perforation should be evaluated for the potential need for additional treatment before coming on study Patients with known immune impairment who may be unable to respond to anti-CTLA-4 antibody Bowel obstruction or any condition precluding oral intake. No gastric tube for venting purposes. No significant gastrointestinal disease or fistula Known active hepatitis infections or active infections require iv systemic antibiotics Patients receiving any medications or substances that are inhibitors or inducers of CYP3A4 are ineligible. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product Patients with uncontrolled intercurrent illness Patients with psychiatric illness/social situations that would limit compliance with study requirements Clinically significant (i.e., active) cardiovascular disease: cerebral vascular accident/stroke (< 6 months prior to enrollment), myocardial infarction (< 6 months prior to enrollment), unstable angina, congestive heart failure (>= New York Heart Association Classification class II), or serious cardiac arrhythmia requiring medication Individuals with a history of a different malignancy are ineligible except for the following circumstances: Individuals with a history of other malignancies are eligible if they have been disease-free for at least 3 years and are deemed by the investigator to be at low risk for recurrence of that malignancy. Individuals with the following cancers are eligible if diagnosed and treated within the past 5 years: breast cancer in situ, cervical cancer in situ, and basal cell or squamous cell carcinoma of the skin Pregnant women are excluded from this study because nivolumab and ipilimumab are immunotherapeutic agents with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with nivolumab and ipilimumab, breastfeeding should be discontinued if the mother is treated with nivolumab and ipilimumab. These potential risks may also apply to other agents used in this study