Anti-Mesothelin TNaive/SCM hYP218 (TNhYP218) CAR T Cells in Participants With Mesothelin-Expressing Solid Tumors Including Mesothelioma

Background: * Mesothelin (MSLN), a cell surface glycoprotein, normally expressed on the mesothelial cells lining the pleura, peritoneum, and pericardium, is highly expressed in many cancers including mesothelioma, ovarian, lung, thymic, colorectal, pancreatic, and gastric cancers, making it an attractive target for immunotherapy. * Adoptive cell therapy using CAR T cells exploits the ability of these modified T cells to recognize and kill their target. Several mesothelin directed CAR T cell therapies have been evaluated in clinical trials, but thus far have not resulted in significant anti-tumor efficacy. * Many antibodies used to make anti-mesothelin CAR T cells bind to the immunogenic distal region of mesothelin, away from the cell membrane. * hYP218 CAR T cells target membrane-proximal region of mesothelin and in pre-clinical studies have shown increased tumor killing and persistence compared to CAR T cells binding to membrane distal region of mesothelin. * Naive/SCM T cells have stem cell like properties and have increased persistence and decreased exhaustion in tumors. * We hypothesize that TNaive/SCM anti-mesothelin, TNhYP218 CAR T cells will have enhanced anti-tumor activity and increased persistence in participants with mesothelioma and other mesothelin expressing cancers. Objectives: * Part 1- Dose escalation: Establish the recommended phase 2 dose (RP2D) of TNhYP218 CAR T cells based on dose-limiting toxicity (DLT) of defined adverse events (AEs). * Part 2- Dose expansion: Determine the preliminary objective response rate of TNhYP218 CAR T cells in a limited number of participants with mesothelioma treated at the RP2D. Eligibility: * Age 18 or older * Must have unresectable, histologically confirmed, recurrent, locally advanced, or metastatic mesothelioma, and other mesothelin expressing solid tumors. * Tumor must be positive for mesothelin in more than half of the cancer cells. * Participants must have an ECOG performance status of 0 or 1. * Participants must have adequate organ function. Design: * Phase 1 dose-escalation study of TNhYP218 CAR T cells, with a small expansion cohort. * Participants will undergo leukapheresis for cell manufacture, followed by lymphodepletion with chemotherapeutic drugs, followed by infusion of TNhYP218 CAR T cells. * Participants will be followed for safety for up to 15 years per FDA requirement.