The purpose of this study is to test the effectiveness of the drugs cabozantinib with nivolumab and ipilimumab in rare genitourinary (GU) cancers that have no standard treatment options.

The combination of these drugs is not currently approved by the U.S. Food and Drug Administration (FDA) and is considered experimental when used for treatment of rare GU cancers. This combination has been tested together in another study and has been proven to be safe with manageable expected toxicities. Therefore, the safe doses have already been established for this combination and that is what will be used in this study. 
   
Cabozantinib is a drug that has been approved by the FDA to treat medullary thyroid cancer. Ipilimumab has been approved by the FDA to treat melanoma and also in combination with nivolumab to treat the most common type of kidney cancer, clear cell carcinoma. Nivolumab has been approved by FDA to treat melanoma, clear cell kidney cancer, and to treat patients with locally advanced or metastatic urothelial carcinoma (the most common type of bladder cancer), who have disease progression during or following platinum-containing chemotherapy or have disease progression within 12 months of neoadjuvant or adjuvant treatment with a platinum-containing chemotherapy.   
   
This study has 12 different groups based on the type of cancer diagnosis for each patient. Based on the type of cancer, participants will be assigned to one of these groups, but all 12 groups will receive the same drugs (combination of cabozantinib, nivolumab and ipilimumab) on the same schedule.

For the first 12 weeks, participants will take cabozantinib by mouth once a day, nivolumab in the vein once every 3 weeks, and ipilimumab in the vein once every 3 weeks. After the first 12 weeks, participants will continue cabozantinib by mouth once a day and will receive nivolumab in the vein once every 4 weeks.

Participants may receive cabozantinib and nivolumab continuously until they have intolerable side effects, or their scan shows worsening disease. In addition, if the disease improves as a result of treatment, and this continues for 2 years on treatment, treatment will be stopped and the disease will be monitored off treatment.

Researchers would also like to better understand the behavior of these rare cancers and to be able to predict who would respond to the treatment and who would not. Therefore, the study doctor will use some of the tissue left over from each participant’s biopsy when they were diagnosed with cancer. If there is not enough tissue left over from the biopsy, another biopsy will be required to get this tissue before starting the treatment.