Mesothelin-Specific T-Cells (FH-TCR-Tᴍsʟɴ) for the Treatment of Metastatic Pancreatic Ductal Adenocarcinoma

Inclusion Criteria: * LEUKAPHERESIS: Tissue confirmation of pancreatic ductal adenocarcinoma and expression of mesothelin (MSLN): Participants must have metastatic disease. Confirmation of diagnosis must be or have been performed by internal pathology review of archival, initial or subsequent biopsy or other pathologic material at Fred Hutchinson Cancer Research Center (Fred Hutch)/University of Washington (UW). Baseline tissue will be stained by immunohistochemistry (IHC) to confirm MSLN expression * LEUKAPHERESIS: Measurable disease by RECIST 1.1 criteria: Participants must have measurable disease. Baseline imaging (for example diagnostic computed tomography \[CT\] chest/abdomen/pelvis) must be obtained within 28 days prior to start of first planned FHMSLN-TCR infusion. Magnetic resonance imaging (MRI) can be substituted for CT in patients unable to have CT contrast * LEUKAPHERESIS: Previous treatment with chemotherapy: Patients may have been previously treated with at least one prior line of systemic therapy for metastatic disease * LEUKAPHERESIS: Human leukocyte antigen (HLA) type HLA-A\*02:01: Participants must be HLA-A\*02:01 in order for the infused transgenic T cells to recognize antigen-major histocompatibility complex (MHC) complexes on their tumor. HLA typing should be determined though a molecular approach in a clinical laboratory licensed for HLA typing * LEUKAPHERESIS: Life expectancy must be \> 3 months at trial entry * LEUKAPHERESIS: 18 years or older * LEUKA…