To learn more about the way the T cells are working in the patient's body, an extra 20-40 mL (4-8 teaspoons) of blood will be taken before each infusion, and at Weeks 1, 2, 4 and 6. Afterwards, blood will be collected at 3, 6, 9 and 12 months after the last infusion. The investigators will use this blood to see how long the T cells last, and to look at the immune response to the patient's response to cancer. Patients will then be contacted once a year for up to 4 additional years (total of 5 years follow-up) to evaluate their disease response long-term.