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. Drugs used in chemotherapy, such as cabozantinib, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. 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.