Metastatic Prostate Small Cell Neuroendocrine Carcinoma

This phase II trial studies how well cabozantinib works in combination with nivolumab and ipilimumab in treating patients with rare genitourinary (GU) tumors that has spread from where it first started (primary site) to other places in the body. Cabozantinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. 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. Giving cabozantinib, nivolumab, and ipilimumab may work better in treating patients with genitourinary tumors that have no treatment options compared to giving cabozantinib, nivolumab, or ipilimumab alone.