T Cell Receptor Immunotherapy Targeting MAGE-A3 for Patients With Metastatic Cancer Who Are HLA-A*01 Positive

Background: * We have constructed a single retroviral vector that contains both alpha and beta chains of a T cell receptor (TCR) that recognizes the human leukocyte antigen serotype within HLA-A "A" serotype group (HLA-A 01) restricted MAGE-A3 tumor antigen, which can be used to mediate genetic transfer of this TCR with high efficiency. * In co-cultures with human leukocyte antigen serotype within HLA-A A serotype group (HLA-A 01) and MAGE-A3 double positive tumors, the anti-MAGE-A3- A 01 restricted (anti-MAGE-A3-01) TCR transduced T cells secreted significant amounts of Interferon (IFN)- \>= with high specificity. Objectives: Primary objectives: * Determine a safe dose of administration of autologous T cells transduced with an anti- MAGE-A3 HLA-A 01-restricted TCR (MAGE-A3-01) TCR and aldesleukin to patients following a nonmyeloablative but lymphoid depleting preparative regimen. * Determine if this approach will result in objective tumor regression in patients with metastatic cancer expressing MAGE-A3. * Determine the toxicity profile of this treatment regimen. Eligibility: Patients who are HLA-A 01 positive and 18 years of age or older must have * Metastatic cancer whose tumors express the MAGE-A3 antigen * Previously received and have been a non-responder to or recurred following at least one first line treatment for metastatic disease Patients may not have: \- Contraindications for high dose aldesleukin administration. Design: * Peripheral blood mononuclear cells (PBMC) obtained by leukapheresis will be transduced with the retroviral vector supernatant encoding the anti-MAGE-A3 HLA-A 01-restricted TCR. * The study will begin with a phase I dose escalation. After the maximum tolerated dose (MTD) cell dose has been determined, patients will be enrolled into the phase II portion of the trial at the MTD established during the phase I portion of the study. In the phase II portion, patients will be entered into two cohorts: cohort 2a will include patients with metastatic melanoma; cohort 2b will include patients with renal cancer and other types of metastatic cancer. * Patients will receive a nonmyeloablative but lymphocyte depleting preparative regimen consisting of cyclophosphamide and fludarabine followed by intravenous infusion of ex vivo tumor reactive, TCR gene-transduced PBMC plus intravenous (IV) aldesleukin. * Patients will undergo complete evaluation of tumor response every 1-6 months until off study criteria are met. * For each of the two strata evaluated in the phase 2 portion, the study will be conducted using a phase II optimal design where initially 21 evaluable patients will be enrolled. For each of these two arms of the trial, if 0 or 1 of the 21 patients experiences a clinical response, then no further patients will be enrolled but if 2 or more of the first 21 evaluable patients enrolled have a clinical response, then accrual will continue until a total of 41 evaluable patients have been enrolled in that stratum. * For both strata, the objective will be to determine if the treatment regimen is able to be associated with a clinical response rate that can rule out 5% (p0=0.05) in favor of a modes 20% partial response (PR) + complete response (CR) rate (p1=0.20). * In order to complete the dose escalation phase and both phase II cohorts, a total of up to 20+82=102 patients may be required (20 + 2 strata with a maximum of 41 apiece). Up to 6 patients enrolled at the MTD will count towards the accrual in the appropriate phase II strata if they are evaluable for response and if they would be fully eligible for enrollment in the phase II portion of the trial. Provided that about 4-5 patients per month will be able to be enrolled onto this trial, approximately 2 to 3 years may be needed to accrue the maximum number of required patients.