Testing Ipilimumab and Nivolumab Combination With or Without Cabozantinib in People >= 18 Years Old With Advanced Soft Tissue Sarcoma

PRIMARY OBJECTIVE: I. Assess progression free survival (PFS) of ipilimumab + nivolumab versus (vs.) the cabozantinib + nivolumab + ipilimumab combination in patients with metastatic, or locally advanced, surgically unresectable soft tissue sarcoma (STS) using Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1. SECONDARY OBJECTIVES: I. Evaluate the response rate (complete response \[CR\]+partial response \[PR\]) of ipilimumab + nivolumab vs. the cabozantinib + nivolumab + ipilimumab combination. II. Evaluate the response rate (CR+PR) of cabozantinib + ipilimumab + nivolumab in (crossover) patients whose disease has progressed on ipilimumab + nivolumab therapy. III. Assess the number of tumor-infiltrating CD8+ T cells in tumor biopsies before and after treatment. EXPLORATORY OBJECTIVES: I. Measure tumor-infiltrating CD3+ T cells and CD68+ macrophages in biopsy specimens. II. Evaluate genomic alterations in circulating tumor DNA (ctDNA) and their potential association with therapy response or resistance. III. Investigate whether response is associated with genetic aberrations and/or tumor mutational burden. IV. Analyze total MET and activated MET (p1235-MET) in biopsy specimens before and after study treatment and evaluate molecular target engagement by cabozantinib (as shown by a lower phosphorylated \[p\]MET/MET ratio). V. Evaluate the objective response rate in patients treated with ipilimumab + nivolumab or the cabozantinib + nivolumab + ipilimumab combination using immune-modified Response Evaluation Criteria in Solid Tumors (iRECIST). OUTLINE: Patients are randomized to 1 of 2 arms. ARM A: Patients receive nivolumab intravenously (IV) over 30-60 minutes and ipilimumab IV over 60-90 minutes on day 1 of each cycle. Treatment repeats every 21 days in the absence of disease progression or unacceptable toxicity for 4 cycles. Patients then receive nivolumab IV over 30 minutes on day 1 of subsequent cycles. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. Patients also undergo computed tomography (CT) or magnetic resonance imaging (MRI) scans, tumor biopsies, and collection of urine samples throughout the trial. Patients may also optionally undergo collection of blood samples at baseline. Patients can crossover from Arm A to Arm B at the time of disease progression. ARM B: Patients receive cabozantinib orally (PO) once daily (QD) or every other day (QOD), nivolumab IV over 30-60 minutes on day 1, and ipilimumab IV over 60-90 minutes on day 1 of each cycle. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity for 4 cycles. Patients then receive nivolumab IV over 30 minutes on day 1 and cabozantinib PO QD or QOD of subsequent cycles. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. Patients crossing over after ≥ 4 ipilimumab + nivolumab (Arm A) cycles will receive cabozantinib and nivolumab only on Arm B; patients that cross over after \< 4 ipilimumab + nivolumab (Arm A) cycles will receive the remaining cycles of ipilimumab (totaling 4 doses) plus nivolumab in combination with cabozantinib. Patients who crossover will start with the every 3 weeks cycle 1 treatment even if they will not be receiving ipilimumab. Patients also undergo CT or MRI scans, tumor biopsies, and collection of urine samples throughout the trial. Patients may also optionally undergo collection of blood samples at baseline. After completion of study treatment, patients are followed for 30 days.