Nivolumab With or Without Ipilimumab in Treating Patients With Gastrointestinal Stromal Tumor That Is Metastatic or Cannot Be Removed by Surgery

PRIMARY OBJECTIVES: I. To assess the response rate of nivolumab alone and in combination with ipilimumab in subjects with metastatic or locally advanced/unresectable gastrointestinal stromal tumor (GIST). SECONDARY OBJECTIVES: I. Ascertain the response rate of nivolumab alone and in combination of ipilimumab in subjects with metastatic or locally advanced/unresectable GIST by Choi criteria. II. Assess the progression-free survival (PFS). III. Ascertain the clinical benefit rate (CBR = complete response \[CR\] + partial response \[PR\] and stable disease \[SD\]) of nivolumab and ipilimumab in refractory/unresectable GIST. IV. Explore the safety of nivolumab monotherapy and nivolumab and ipilimumab in this population assessed by the frequency and severity of adverse events (AEs). TERTIARY OBJECTIVES: I. Compare RR and CBR in patients whose tumors are programmed cell death ligand 1 (PD-L1) positive (+) and PD-L1 negative (-) at baseline. II. In the patients who are PD-L1 positive, compare RR and CBR in patients with 1% and 5% tumor membrane staining. III. Determine the baseline mutational load of patients at the start of treatment. IV. Determine the response to treatment based on the baseline mutation load and baseline GIST mutations. V. Determine the response rate based on GIST mutational status. OUTLINE: Patients are randomized to 1 of 2 arms. ARM I: Patients receive nivolumab intravenously (IV) over 60 minutes on day 1. Courses repeat every 14 days for up to 2 years in the absence of disease progression or unacceptable toxicity. ARM II: Patients receive nivolumab IV over 30 minutes on day 1 and ipilimumab IV over 30 minutes every 6 weeks. Courses repeat every 14 days for up to 2 years in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up periodically.