TAA Specific Cytotoxic T Lymphocytes in Patients With Pancreatic Cancer

Status - CLOSED TO PATIENT ENROLLMENT (CNPE) The patient will give blood to make TAA-Specific cytotoxic T cells in a lab. These cells well be grown and frozen. If the TAA-Specific cytotoxic T cells can be made, the time from collection of the blood to manufacture of T cells for administration to the patient is about 1 to 2 months. The cells will be infused by intravenous infusion (IV) into the patient over 1-10 minutes. The patient may be pre-treated with acetaminophen (Tylenol) and diphenhydramine (Benadryl). Acetaminophen (Tylenol) and diphenhydramine (Benadryl) are given to prevent a possible allergic reaction to the TAA-CTL administration. Patients will be given up to six doses of TAA-CTLs at monthly intervals. The treatments will be given by the Center for Cell and Gene Therapy at Houston Methodist Hospital (HMH). MEDICAL TESTS BEFORE TREATMENT: * Physical exam. * Blood tests to measure blood cells, kidney and liver function. * Measurements of the patient's tumor by routine imaging studies and/or blood tests. The study will use the imaging study that was used before to follow the patient's tumor: CT, MRI, or PET. * Blood test to check for pregnancy for female patients who can have children MEDICAL TESTS DURING TREATMENT: Standard medical tests will be conducted on the day of the second and subsequent infusions: * Physical exams prior to each T cell infusion * Blood tests to measure blood cells, kidney and liver function. MEDICAL TESTS AFTER TREATMENT: \- Measurements the patient's tumor by routine imaging studies and/or blood tests done as per standard of care. To learn more about the way the TAA-CTLs are working in patient's body, an extra 20-40 mL (4-8 teaspoons) of blood will be taken before the infusion, at Weeks 1 and 2 after each infusion and at weeks 4, 6 and 8 and months 3, 6, 9 and 12 after the last infusion. The blood may be drawn from a central line at the time of the patient's regular blood tests. Investigators will use this blood to see how long the TAA-CTLs last, and to look at the immune system response to the patient's cancer. Study Duration: Patients will be active participants in this study for approximately one year after their last dose. Investigators will contact patients once a year for up to 4 additional years (total of 5 years follow-up) in order to evaluate disease response long-term. \*Arm A and Arm B are closed to new patient enrollment.\*