A Study of Nivolumab in Selected Uterine Cancer Patients

Inclusion Criteria: * Histologically confirmed diagnosis of metastatic or recurrent uterine cancer (endometrial carcinoma, carcinosarcoma, clear cell carcinoma, leiomyosarcoma, undifferentiated sarcoma, high grade endometrial stromal sarcoma) by Memorial Sloan Kettering Cancer Center. Carcinosarcomas, endometrioid and clear cell carcinomas that appears to have arisen in the ovary/fallopian tube or peritoneum are also eligible. Recurrence should not be amenable to curative approaches such as surgical resection or chemoradiotherapy. * Tumor is confirmed to be one of the following: 1. MSI-high, or 2. MMR-deficient, or 3. Hypermutated defined as ≥20 somatic mutations in the tumor by MSK-IMPACT * One or more prior lines of cytotoxic treatment for advanced disease (prior hormonal therapy is not considered to count as prior lines of therapy) * Measurable disease by RECIST 1.1 criteria * No known CNS metastases * ECOG Performance status 0-1 * ECOG Performance status 0-1 * WBC ≥ 2000/uL, ANC ≥ 1500/uL, PLT ≥ 100,000/uL, HGB ≥ 8 g/dL * Serum creatinine ≤ 1.5 x ULN or creatinine clearance of ≥ 40mL/min by Cockroft-Gault formula * AST (SGOT) and ALT (SGPT) ≤ 3 x ULN * Total bilirubin ≤ 1.5 x ULN, except subjects with Gilbert's syndrome who can have total bilirubin ≤ 3.0 mg/dL * Able to sign voluntary written informed consent * Female, 18 years of age or older * Available archival tumor tissue or patient is willing to undergo new biopsy * Premenopausal women of child bearing potential must have a normal urine or serum beta-HCG prior to enrollment, and must agree to use effective contraception during treatment with nivolumab and for at least 5 months following the last dose of nivolumab. Exclusion Criteria: * Disease eligible for potentially curative treatment with standard chemotherapy, surgical resection, or chemoradiotherapy. * Known or suspected autoimmune disease, except for subjects with vitiligo, diabetes mellitus, resolved childhood asthma/atopy, residual hypothyroidism due to an autoimmune immune condition only requiring thyroid hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger. * Serious uncontrolled medical disorder or active infection which would impair the ability of the subject to receive protocol therapy or whose control would be jeopardized by protocol therapy * History of bowel obstruction, refractory ascites, or bowel perforation due to advanced disease within the past 3 months from start of study treatment. * Prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, anti-CTLA-4 antibody or any other antibody or drug specifically targeting T cell co-stimulation or immune checkpoint pathways * Patients who have a condition that requires systemic treatment with either corticosteroids within 7 days of enrollment (systemic corticosteroid therapy is defined as \>10 mg daily prednisone or its equivalent); or who require 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. * Prior history of malignancy or a concurrent malignancy, with the exception of cutaneous basal cell carcinoma or squamous cell carcinoma, superficial bladder cancer, or in situ carcinoma of the uterine cervix, prostate, or breast, unless a complete remission was achieved at least 3 years prior to study entry and no additional therapy is required or anticipated to be required during the study period * Breastfeeding women, pregnant women * Prisoners or subjects who are involuntarily incarcerated * Subjects who are compulsorily detained for treatment of either a psychiatric or physical illness * Positive test for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV antibody) indicating acute or chronic infection (if patient has documented Hepatitis B and C from within 6 months of enrollment, these tests do not need to be repeated.) * Known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) * Known allergy or Adverse Drug Reaction to nivolumab, or a history of allergy to study drug components.