BrUOG 354 Nivolumab +/- Ipilimumab for Ovarian and Extra-renal Clear Cell Carcinomas

Inclusion Criteria: * Patients must have a recurrent, advanced, or metastatic pure clear cell carcinoma of ovarian, fallopian tube, primary peritoneal, or extra-renal origin. * All patients must submit representative tissue from their malignancy. * Participants must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as ≥20 mm with conventional techniques or as ≥10 mm with spiral CT scan, MRI, or calipers by clinical exam. * Patients with a clear cell carcinoma of ovarian, fallopian or primary peritoneal origin must have progressed after at least one prior platinum and taxane based chemotherapy regimen. Patients with extra-renal clear cell cancer (including other GYN) cancers must have progressed after at least one prior regimen for advanced/metastatic disease. Radiation therapy (including the use of chemotherapy as a radiosensitizer) will not count as a prior systemic regimen. * No prior anti-PD-1, PD-L1 or CTLA-4 antibody. * Age ≥ 18 * ECOG performance status 0 to 1 * Participants must have normal organ and marrow function as defined below: leukocytes ≥3,000/mcL absolute neutrophil count ≥1,500/mcL platelets ≥100,000/mcL total bilirubin within normal institutional limits EXCEPTIONS: conjugated hyperbilirubinemia; Gilbert's syndrome, both of which will allow a total bilirubin \<3.0mg/dL \<5xULN is liver metastases are present A value below the LLN is acceptable if confirmed appropriate by the treating MD AST(SGOT)/ALT(SGPT) ≤2.5 × institutional upper limit of normal creatinine ≤ 1.5 X ULN (upper limit of normal) OR creatinine clearance ≥50 mL/min * Adequate thyroid function within 28 days prior to registration defined as serum TSH in normal range. Patients on thyroid hormone supplementation are allowed provided the serum TSH is within normal limits. * Subjects must have a resting baseline O2 saturation by pulse oximetry of ≥92% at rest. This should be documented within two weeks of registration. * Reproductive status: * Women of childbearing potential (WOCBP) must use method(s) of contraception. Given there is insufficient information to assess teratogenicity (preclinical studies have not been done), a highly effective method(s) of contraception (failure rate of less than 1% per year) is required as determined by the treating investigator. WOCBP must follow instructions for birth control. For all women who discontinue protocol treatment, contraception should be continued for five months following the last dose of therapy. * WOCBP must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 7 days prior to the start of registration. * Women who are not of childbearing potential (ie, who are postmenopausal (lack of menses \> 24 months) or surgically sterile) and azospermic men do not require contraception. * Women must not be breastfeeding (document for all). * Men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1 % per year. The investigator shall review contraception methods and the time period that contraception must be followed. * Men that are sexually active with WOCBP must follow instructions for birth control when the half life of the investigational drug is greater than 24 hours, contraception should be continued for a period of 7 months after discontinuation of treatment. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Participants who have had prior therapy with nivolumab or 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 check point pathways. * Participants who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study. Patients using endocrine therapy as treatment for their index cancer must be off of treatment for one week (7 days) prior to entering the study. * Participants who have not recovered from clinically significant adverse events to \<grade 2 and which are related to prior treatment agents administered. * Participants who are receiving any other investigational agents. * Participants with known brain metastases are excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * History of severe hypersensitivity reaction to any monoclonal antibody. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection requiring antibiotics, symptomatic congestive heart failure, unstable angina pectoris, serious cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant women are excluded from this study * Patients with a history of other invasive malignancies, with the exception of non-melanoma skin cancer are excluded if there is any evidence of other malignancy being present within the last three years. However, patients with a malignancy that is not-likely to require treatment in the next 2 years, such as a completely resected, early stage breast cancer, are eligible. * Patients who have received prior chemotherapy within the last three years for any other cancer other than for clear cell cancer. * In order for patients with known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) to be eligible, they must be on a stable highly active antiretroviral therapy (HAART) regimen, have CD4 counts \> 350, with no detectable viral load on quantitative PCR within 4 weeks of registration. * Patients with treated hepatitis virus infections (Hepatitis B or Hepatitis C) are eligible if they have been definitively treated for 6 months, have no detectable viral load on quantitative PCR, and LFTs meet eligibility requirements within 4 weeks of screening. * 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. * 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 day 1 study drug administration. * Any other medical condition that will prevent the safe administration of study drugs in the opinion of the treating physician. * Planned concomitant, non-protocol directed anti-cancer therapy during the trial. * Grade ≥2 peripheral neuropathy