Administration of Autologous T-Cells Genetically Engineered to Express T-Cell Receptors Reactive Against Mutated or Viral Neoantigens in a Patient With Metastatic Cancer Plus the Administration of Pembrolizumab

Background: A cancer treatment has been developed called "gene transfer" or "gene therapy." It involves taking white blood cells from a person (called apheresis), genetically modifying the cells in a lab to recognize cancer, and then giving the cells back to the person. Researchers want to see if this treatment can help people with metastatic squamous cell anal cancer. Objective: To see if treating cancer with a person s own white blood cells that have been genetically modified can cause tumors to shrink. Eligibility: People who have metastatic squamous cell anal cancer for which standard treatments have not worked. Design: Participants will have had a tumor biopsy and apheresis to collect white blood cells under a separate protocol. Participants will stay at the hospital for 3 to 4 weeks. They will have an intravenous (IV) catheter placed in a large vein in the upper chest. Participants will get chemotherapy drugs (fludarabine and cyclophosphamide), the cell infusion, and aldesleukin through the IV. Pembrolizumab is given before and for three doses given every three weeks after the cell infusion. Aldesleukin will help the cells grow. Participants will take an antibiotic, antiviral, and antifungal by mouth. They will get an injection of filgrastim. It will stimulate the formation of white blood cells. Participants will have blood and urine tests. They will have physical exams. Their symptoms will be reviewed. They will have imaging scans. About 6 and 12 weeks after they finish treatment, participants will have safety follow-up visits. These visits will take 1 to 2 days. Participants will return to the Clinical Center every 3 to 6 months for 3 years, and then as determined by their doctor. They will be followed long term for up to 15 years on a separate study.