T Cell Receptor Immunotherapy Targeting MAGE-A3 for Patients With Metastatic Cancer Who Are HLA-DP0401 Positive

Background: * We have constructed a single retroviral vector that contains both and $ \<= chains of a T cell receptor (TCR) that recognizes the DP0401/0402 restricted Melanoma antigen family A, 3 (MAGE-A3) tumor antigen, which can be used to mediate genetic transfer of this TCR with high efficiency. * In co-cultures with HLA-DP0401/0402 and MAGE-A3 double positive tumors, the anti- MAGE-A3- DP0401/0402 restricted (anti-MAGE-A3-DP4) TCR transduced T cells secreted significant amounts of Interferon gamma (IFN-y) with high specificity. Objectives: Primary objectives: * Determine a safe dose of the administration of autologous cluster of differentiation 4 (CD4) cells transduced with an anti-MAGE-A3-DP0401/0402 restricted (MAGE-A3-DP4) 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-DP4. * Determine the toxicity profile of this treatment regimen. Eligibility: Patients who are human leukocyte antigens (HLA)-DP0401/0402 positive and 18 years of age or older must have * Metastatic cancer whose tumors express the MAGE-A3-DP4 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: * PBMC obtained by leukapheresis will be enriched for CD4 cells and transduced with the retroviral vector supernatant encoding the anti-MAGE-A3-DP4 TCR. * The study will begin in a standard phase 1 dose escalation. After the maximum tolerated dose (MTD) cell dose has been determined, patients will be enrolled into the phase 2 portion of the trial at the MTD established during the phase 1 portion of the study. In the phase 2 portion, patients will be entered into two cohorts: cohort 1 will include patients with metastatic melanoma; cohort 2 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 peripheral blood mononuclear cells (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 2 strata evaluated in the phase 2 portion, the study will be conducted using a phase 2 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 modest 20% partial response (PR) + complete response (CR) rate (p1=0.20).