Recombinant Interleukin-15 in Combination With Checkpoint Inhibitors Nivolumab and Ipilimumab in People With Refractory Cancers

Background: The drug Interleukin-15 (IL-15) activates the immune system. The drugs nivolumab and ipilimumab unblock immune cells. The drugs together may allow immune cells to recognize and attack cancer cells, causing tumors to shrink. Objective: To test the effects and maximum dose of IL-15, nivolumab, and ipilimumab. Eligibility: People ages 18 and older who have cancer that does not respond to treatment Design: Participants will be screened with: * Medical history * Physical exam * Heart, blood, and urine tests * Scans Tumor biopsy: A small needle removes a tumor sample. Participants will be in 1 of 3 treatment groups: * IL-15 with nivolumab * IL-15 with ipilimumab * IL-15 with nivolumab and ipilimumab Participants will take the drugs in four 6-week cycles. IL-15 is injected under the skin. The other two drugs are injected into an arm vein over 60-90 minutes. Participants may need to stay at the hospital 2-3 hours after the first dose of any drug to watch for side effects. Each cycle will include: * Weekly blood and urine tests * 16 IL-15 injections * 1 ipilimumab injection if applicable * 3 nivolumab injections if applicable * Blood tests weekly during cycles 1 and 2 * Urine tests weekly during cycles 1 and 2 * Scans and a tumor biopsy on day 42 After cycle 4, participants will stop taking IL-15. They will continue the other drugs until they can no longer tolerate the side effects, or their cancer gets worse. Those cycles will include: * 1 ipilimumab injection if applicable * 3 nivolumab injections if applicable * Scans every other cycle After participants stop treatment, their doctor will monitor their side effects for 4 months or until they go away.