Recurrent Melanoma

This phase II trial studies the good and bad effects of the combination of drugs called cabozantinib and nivolumab in treating patients with melanoma or squamous cell head and neck cancer that may have spread from where it first started to nearby tissue, lymph nodes, or distant parts of the body (advanced). 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, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. This trial may help doctors determine how quickly patients can be divided into groups based on biomarkers in their tumors. A biomarker is a biological molecule found in the blood, other body fluids, or in tissues that is a sign of a normal or abnormal process or a sign of a condition or disease. A biomarker may be used to see how well the body responds to a treatment for a disease or condition. The two biomarkers that this trial is studying are "tumor mutational burden" and "tumor inflammation signature." Another purpose of this trial is to help doctors learn if cabozantinib and nivolumab shrink or stabilize the cancer, and whether patients respond differently to the combination depending on the status of the biomarkers.

To find the highest tolerable dose and recommended dose of PRAME-TCR-NK cells that can be given to participants with recurrent and/or refractory melanoma. The safety and tolerability of PRAME-TCR-NK cells will also be studied.