This phase II trial tests whether the combination of nivolumab and ipilimumab is better than nivolumab alone to shrink tumors in patients with deficient mismatch repair system (dMMR) endometrial carcinoma that has come back after a period of time during which the cancer could not be detected (recurrent). Deoxyribonucleic acid (DNA) mismatch repair (MMR) is a system for recognizing and repairing damaged DNA. In 2-3% of endometrial cancers this may be due to a hereditary condition resulted from gene mutation called Lynch Syndrome (previously called hereditary nonpolyposis colorectal cancer or HNPCC). MMR deficient cells usually have many DNA mutations. Tumors that have evidence of mismatch repair deficiency tend to be more sensitive to immunotherapy. There is some evidence that nivolumab with ipilimumab can shrink or stabilize cancers with deficient mismatch repair system. However, it is not known whether this will happen in endometrial cancer; therefore, this study is designed to answer that question. Monoclonal antibodies, such as nivolumab and ipilimumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Giving nivolumab in combination with ipilimumab may be better than nivolumab alone in treating dMMR recurrent endometrial carcinoma.

PRIMARY OBJECTIVE: I. To assess efficacy in terms of progression-free survival (PFS) for immunotherapy with dual immune checkpoint blockade (nivolumab/ipilimumab) versus (vs.) monotherapy (nivolumab) in patients with recurrent mismatch repair (MMR) deficient endometrial carcinoma with measurable or non-measurable (detectable) disease. SECONDARY OBJECTIVES: I. To evaluate the overall survival (OS) as estimated from time of enrollment to last follow-up or death. II. To evaluate the objective response rate by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 in those with measurable disease at start of treatment. III. To evaluate progression-free survival at 6 months. IV. To evaluate the nature, frequency and degree of toxicity as assessed by the Common Terminology Criteria for Adverse Events (CTCAE) version (v) 5.0. V. To evaluate PFS and objective response rate in patients with prior anti-PD1/PDL1 therapy and compare efficacy of dual immune checkpoint inhibition vs. anti-PD1 monotherapy. OUTLINE: Patients are randomized into 1 of 2 arms. ARM I: Patients receive nivolumab intravenously (IV) over 30 minutes on day 1 of each cycle and ipilimumab IV over 90 minutes on day 1 of every other cycle. Cycles repeat every three weeks. Treatment with nivolumab and ipilimumab repeats for up to 8 cycles in the absence of disease progression, unacceptable toxicity, or complete response (CR). Patients then receive nivolumab alone on day 1 of each cycle. Cycles repeat every 4 weeks in the absence of disease progression, unacceptable toxicity, or CR. ARM II: Patients receive nivolumab IV over 30 minutes on day 1 of each cycle. Treatment repeats every 3 weeks for up to 8 cycles, then every 4 weeks thereafter in the absence of disease progression, unacceptable toxicity, or CR. MAINTENANCE THERAPY: Patients achieving CR on Arm I or II receive nivolumab for an additional 12 months in the absence of disease progression or unacceptable toxicity. Additionally, all patients may optionally undergo collection of tissue samples on study as well as blood samples throughout the trial. All patients also undergo computed tomography (CT) scan and/or magnetic resonance imaging (MRI) throughout the trial. Patients are followed every 3 months for 2 years, and then, every 6 months for 3 years.