After the antigen-escalation phase, the dose-escalation phase will begin. Patients will be started on the lowest dose (1 of 3 different levels) of T cells. Once that dose schedule proves safe, the next group of patients will be started at a higher dose. This process will continue until all 3 dose levels are studied. If the side-effects are too severe, the dose will be lowered or the T cell injections will be stopped.