This phase III trial compares the usual treatment (treatment with ipilimumab and nivolumab followed by nivolumab alone) to treatment with ipilimumab and nivolumab, followed by nivolumab with cabozantinib in patients with untreated renal cell carcinoma that has spread to other parts of the body. The addition of cabozantinib to the usual treatment may make it work better. Immunotherapy with 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. Cabozantinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. It is not yet known how well the combination of cabozantinib and nivolumab after initial treatment with ipilimumab and nivolumab works in treating patients with renal cell cancer that has spread to other parts of the body.

PRIMARY OBJECTIVE: I. To compare the overall survival (OS) in patients with metastatic renal cell cancer (RCC) treated with ipilimumab-nivolumab followed by either nivolumab versus cabozantinib-nivolumab. SECONDARY OBJECTIVES: I. To determine progression free survival (PFS) of patients treated with nivolumab versus nivolumab-cabozantinib. II. To evaluate the 12-month complete response rate in patients treated with ipilimumab-nivolumab followed by cabozantinib-nivolumab versus ipilimumab-nivolumab followed by nivolumab (patients who have complete response \[CR\] and relapse before 12 months will not be counted as a CR at 12-months). III. To evaluate the rates of discontinuing therapy at 1 year. IV. To compare objective response rates (ORR, assessed by Response Evaluation Criteria in Solid Tumors \[RECIST\] 1.1 and Immune Response Evaluation Criteria in Solid Tumors \[iRECIST\] criteria) for patients treated with ipilimumab-nivolumab followed by cabozantinib-nivolumab versus ipilimumab-nivolumab followed by nivolumab. V. To document the adverse event profile of ipilimumab-nivolumab followed by cabozantinib-nivolumab. BIOMARKER OBJECTIVES: I. To evaluate biomarkers associated with exceptional responses in both arms (exceptional responses defined as CRs with treatment discontinuation at 12 months or 24 months). II. To evaluate whether baseline IL-6 is predictive of outcome in patients treated with cabozantinib-containing regimen. QUALITY OF LIFE (QOL) OBJECTIVES: I. To compare health-related quality of life at 18 months post-registration as assessed by the Functional Assessment of Cancer Therapy (FACT)-Kidney Symptom Index 19 (FKSI-19) between patients randomized to nivolumab (nivo) versus (vs) cabozantinib (cabo)/nivo. II. To compare health-related quality of life as assessed by the FKSI-19 between patients randomized to nivo vs cabo/nivo at other time points. III. To compare patient-reported fatigue using Patient-Reported Outcomes Measurement Information System (PROMIS)-Fatigue between patients randomized to nivo vs cabo/nivo. IV. To compare quality-adjusted survival (overall survival x utility score assessed by EuroQol five-dimensional questionnaire \[EQ5D-5L\]) between patients randomized to nivo vs cabo/nivo. OUTLINE: INDUCTION: Patients receive nivolumab intravenously (IV) over 30 minutes and ipilimumab IV over 30 minutes on day 1. Treatment repeats every 21 days for up to 4 cycles in the absence of disease progression or unacceptable toxicity. TREATMENT: Patients with unconfirmed but clinical progression of disease (iuPD) with clinical instability receive cabozantinib orally (PO) daily on days 1-28. Treatment repeats every 28 days until further disease progression or unacceptable toxicity. Patients with unconfirmed CR (iCR) receive nivolumab IV between 30-60 minutes on day 1. Treatment repeats every 28 days in the absence of disease progression or unacceptable toxicity. Patients with non-CR/non-PD or iuPD with clinical stability are randomized to 1 of 2 arms. ARM A: Patients receive nivolumab IV between 30-60 minutes on day 1. Treatment repeats every 28 days in the absence of disease progression or unacceptable toxicity. ARM B: Patients receive nivolumab IV between 30-60 minutes on day 1 and cabozantinib PO daily on days 1-28. Treatment repeats every 28 days in the absence of disease progression or unacceptable toxicity. Patients undergo computed tomography (CT) scan, magnetic resonance imaging (MRI) and blood and urine sample collection, and may also undergo a bone scan as clinically indicated throughout the study.