Autologous T-cells Genetically Engineered to Express Receptors Reactive Against KRAS Mutations in Conjunction With a Vaccine Directed Against These Antigens in Participants With Metastatic Cancer

Background: Many cancer cells produce substances called antigens that are unique to each cancer. These antigens stimulate the body s immune responses. One approach to treating these cancers is to take disease-fighting white blood cells from a person, change those cells so they will target the specific proteins (called antigens) from the cancer cells, and return them to that person s blood. The use of the white blood cells in this manner is one form of gene therapy. A vaccine may help these modified white cells work better. Objective: To test a cancer treatment that uses a person s own modified white blood cells along with a vaccine that targets a specific protein. Eligibility: Adults aged 18 to 72 years with certain solid tumors that have spread after treatment. Design: Participants will undergo leukapheresis: Blood is removed from the body through a tube attached to a needle inserted into a vein. The blood passes through a machine that separates out the white blood cells. The remaining blood is returned to the body through a second needle. Participants will stay in the hospital for 3 or 4 weeks. They will take chemotherapy drugs for 1 week to prepare for the treatment. Then their modified white cells will be infused through a needle in the arm. They will take other drugs to prevent infections after the infusion. The vaccine is injected into a muscle; participants will receive their first dose of the vaccine on the same day as their cell infusion. Participants will have follow-up visits 4, 8, and 12 weeks after the cell infusions. They will receive 2 or 3 additional doses of the boost vaccine during these visits. Follow-up will continue for 5 years, but participants will need to stay in touch with the gene therapy team for 15 years. ...

* INCLUSION CRITERIA: * Participants with an appropriate HLA match for available Surgery Branch KRAS TCRs with evaluable metastatic solid cancer (e.g., gastrointestinal, genitourinary, breast, ovarian, non-small cell lung cancer (NSCLC) and other solid cancers) with known KRAS G12V or G12D mutation. * Confirmation of diagnosis of cancer by the NCI Laboratory of Pathology. * Refractory to standard systemic therapy. Specifically: * Participants with metastatic colorectal cancer must have received oxaliplatin and/or irinotecan. * Participants with breast and ovarian cancer must have received at least two systemic treatments. * Participants with NSCLC must have received at least one platinum-based chemotherapy regimen and at least one FDA-approved targeted treatment (when appropriate). * Participants with other solid tumors must have received at least one prior line of systemic treatment or have declined standard treatment. * Participants with three (3) or fewer brain metastases that are \< 1 cm in diameter each and asymptomatic are eligible. Lesions that have been treated with stereotactic radiosurgery must be clinically stable for one month after treatment for the participant to be eligible. Participants with surgically resected brain metastases are eligible. * Age \>= 18 years and \ 1000/mm\^3 without growth factor support * WBC \>= 2500/mm\^3 * Platelet count (Bullet) 80,000/mm3 * Hemoglobin \> 8.0 g/dL. Subjects may be transfused to reach this cut-off. * Chemistry: * Serum ALT/AST \