Phase II Study of Metastatic Cancer That Overexpresses P53 Using Lymphodepleting Conditioning Followed by Infusion of Anti-P53 TCR-Gene Engineered Lymphocytes

Inclusion Criteria:

* Patients must have metastatic cancer that overexpresses p53 as assessed by immunohistochemistry, as determined by positive staining of tumor sample. when compared to negative controls per procedure in Appendix 1. The immunohistochemical staining will be performed in the Pathology Laboratory Center for Cancer Research (CCR), National Cancer Institute (NCI) on fresh or archival tissue and will be supervised by Dr. Maria Merino. The criteria used to determine overexpression will be that used in the Laboratory of Dr. Curt Harris. Ten fields will be evaluated at 40 X magnification and if greater than 5% of cells stain positive, the tumor will be categorized as an overexpressor.
* Patients with melanoma or renal cell cancer must have previously received interleukin-2 (IL-2) and have been either non-responders (progressive disease) or have recurred. Patients with other histologies,not including hematologic malignancies, must have previously received first line and second line or higher systemic standard care(or effective salvage chemotherapy regimens) for metastatic disease,if known to be effective for that disease and have been either non-responders (progressive disease) or have recurred.
* Age greater than or equal to 18 years.
* Clinical performance status of Eastern Cooperative Oncology Group (ECOG) 0 to 1.
* Life expectancy of greater than three months.
* Seronegative for human immunodeficiency virus (HIV) antibody. (The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who are HIV seropositive can have decreased immune competence and thus be less responsive to the experimental and more susceptible to its toxicities).
* Seronegative for hepatitis B antigen and hepatitis C antibody unless antigen negative.
* Patients must be human leukocyte antigen A(HLA-A) 0201 positive.
* Patients of both genders must be willing to practice birth control for four months after receiving the preparative regimen.
* Absolute neutrophil count greater than 1000/mm\^3, and normal white blood cells (WBC) (greater than 3000/mm\^3).
* Platelet count greater than 100,000/mm\^3.
* Hemoglobin greater than 8.0 g/dl.
* Serum alanine aminotransferase (ALT)/aspartate aminotransferase (AST) less than the upper limit of normal.
* Serum creatinine less than or equal to 1.6 mg/dl.
* Total bilirubin less than or equal to 1.5 mg/dl, except in patients with Gilbert's Syndrome who must have a total bilirubin less than 3.0 mg/dl.
* More than four weeks must have elapsed since any prior systemic therapy at the time the patient receives the preparative regimen, and patients toxicities must have recovered to a grade 1 or less (except for toxicities such as alopecia or vitiligo). Six weeks must have elapsed since prior Ipilimumab (MDX-010) therapy to allow antibody levels to decline, and patients who have previously received MDX-010 must have a normal colonoscopy with normal colonic biopsies.
* Women of child-bearing potential must have a negative pregnancy test because of the potentially dangerous effects of the preparative chemotherapy on the fetus.
* A biopsy must be evaluable to evaluate p53 expression and to confirm the diagnosis by the Laboratory of Pathology, CCR, NCI.

Exclusion Criteria:

* Patients requiring systemic steroid therapy
* Patients with active systemic infections, coagulation disorders or other major medical illnesses of the cardiovascular, respiratory or immune system, myocardial infarction, cardiac arrhythmias, obstructive or restrictive pulmonary disease.
* Patients with any form of primary immunodeficiency (such as Severe Combined Immunodeficiency Disease and acquired immune deficiency syndrome (AIDS)). Patients with opportunistic infections will be excluded. (The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who have decreased immune competence may be less responsive to the experimental treatment and more susceptible to its toxicities).
* Patients with history of severe immediate hypersensitivity reaction to any of the agents used in this study.
* Patient is not willing to sign a durable power of attorney.
* Patient is not able to understand and sign the Informed Consent Document.
* Since aldesleukin will be excluded if they have a history of electrocardio- gram (EKG) abnormalities, symptoms of cardiac ischemia or arrhythmias and have a left ventricular ejection fraction (LVEF) less than 45% on a cardiac stress test (stress thallium, stress multi-gated acquisition scan (MUGA), dobutamine echocardiogram, or other stress test).
* Similarly, patients who are greater than or equal to 50 years old with a LVEF less than 45% will be excluded.
* Patients with a prolonged history of cigarette smoking (greater than 20 pack/year within the past 2 years) or symptoms of respiratory dysfunction (e.g. grade 2 dyspnea or hypoxia) who do not have a normal pulmonary function test as evidenced by a FEV(1) less than 60% predicted will be excluded.