- The study will be conducted using a Phase I/II optimal design. The protocol will proceed in a phase 1 dose escalation design. Initially, the protocol will enroll 1 patient in each dose cohort unless that patient experiences a dose limiting toxicity (DLT). Should a single patient experience a dose limiting toxicity due to the cell transfer at a particular dose level, additional patients would be treated at that dose to confirm that no greater than 1/6 patients have a DLT prior to proceeding to the next higher level. If a level with 2 or more DLTs in 3-6 patients has been identified, three additional patients will be accrued at the next-lowest dose, for a total of 6, in order to further characterize the safety of the maximum tolerated dose prior to starting the phase II portion. If a dose limiting toxicity occurs in the first cohort, that cohort will be expanded to 6 patients. If 2 DLTs are encountered in this cohort, the study will be terminated. If IFN-gamma levels increase substantially (as defined in the protocol) in the patient in a cohort compared to the prior patient, the cohort would be expanded to an n=3 to obtain more data on this phenomenon. If one of these 3 patients experience a DLT, the cohort will be expanded to six patients. Following amendment C, patients will be enrolled in cohorts 8-11, with the non-myeloablative chemotherapy regimen, cells and low dose aldesleukin following a conventional 3+3 design. Once the maximum tolerated dose (MTD) has been determined, the study then would proceed to the phase II portion. Patients will be entered into two cohorts based on histology: cohort 1 will include patients with metastatic melanoma and renal cancer, and cohort 2 will include patients with other types of metastatic cancer.