Gene Modified Immune Cells After Conditioning Regimen for the Treatment of Stage IIIC or IV Melanoma or Metastatic Solid Tumors

This phase I trial studies the side effects and best dose of modified immune cells (IL13Ralpha2 CAR T cells) after a chemotherapy conditioning regimen for the treatment of patients with stage IIIC or IV melanoma or solid tumors that have spread to other places in the body (metastatic). The study agent is called IL13Ralpha2 CAR T cells. T cells are a special type of white blood cell (immune cells) that have the ability to kill tumor cells. The T cells are obtained from the patient's own blood, grown in a laboratory, and modified by adding the IL13Ralpha2 CAR gene. The IL13Ralpha2 CAR gene is inserted into T cells with a virus called a lentivirus. The lentivirus allows cells to make the IL13Ralpha2 CAR protein. This CAR has been designed to bind to a protein on the surface of tumor cells called IL13Ralpha2. This study is being done to determine the dose at which the gene-modified immune cells are safe, how long the cells stay in the body, and if the cells are able to attack the cancer.