The antigen-escalation phase will be first. Patients will receive TAA-specific T cells targeting first 1 and then 2 TAAs. Once this schedule proves safe, the next group of patients will receive TAA-specific T cells targeting first 2 and then 3 TAAs. This process will continue until all 4 levels are studied. This means that the final cohort of patients will receive TAA-specific T cells targeting first 4 and then 5 TAAs. If the side-effects are too severe, the number of TAAs being targeted will be lowered or the T cell injections will be stopped.