Anti-NY ESO-1 mTCR Peripheral Blood Lymphocytes

Inclusion Criteria: * Measurable metastatic cancer that expresses NY ESO-1 as assessed by one of the following methods: reverse transcriptase-polymerase chain reaction (RT-PCR) on tumor tissue, or by immunohistochemistry of resected tissue, or serum antibody reactive with ESO * Confirmation of diagnosis of metastatic cancer by the Laboratory of Pathology at the Montefiore Medical Center * Patients must have previously received 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 * 3 or fewer brain metastases; Note: if lesions are symptomatic or greater than or equal to 1 cm each, these lesions must have been treated and stable for 3 months for the patient to be eligible * 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); Note: patients may have undergone minor surgical procedures within the past 3 weeks, as long as all toxicities have recovered to grade 1 or less or as specified in the eligibility criteria * Eight weeks must have elapsed from the time of any antibody therapy that could affect an anti-cancer immune response, including anti-cytotoxic T-lymphocyte-associated protein 4 (CTLA 4) therapy, at the time the patient receives the preparative regimen to allow antibody levels to decline; Note: patients who have previously received ipilimumab and have documented gastrointestinal (GI) toxicity must have a normal colonoscopy with normal colonic biopsies * Willing to sign a durable power of attorney * Able to understand and sign the informed consent document * Clinical performance status of Eastern Cooperative Oncology Group (ECOG) 0 or 1 * Life expectancy of greater than three months * Patients must be HLA-A\*0201 positive * Patients of both genders must be willing to practice birth control from the time of enrollment on this study and for up to four months after cells are no longer detected in the blood * Serology: * 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 treatment and more susceptible to its toxicities) * Seronegative for hepatitis B antigen, and seronegative for hepatitis C antibody; if hepatitis C antibody test is positive, then patient must be tested for the presence of antigen by RT-PCR and be hepatitis C virus (HCV) ribonucleic acid (RNA) negative * Women of child-bearing potential must have a negative pregnancy test because of the potentially dangerous effects of the treatment on the fetus * Absolute neutrophil count greater than 1000/mm\^3 without the support of filgrastim * White blood cell (WBC) \>= 3000/mm\^3 * Platelet count \>= 100,000/mm\^3 * Hemoglobin \> 8.0 g/dl * Serum alanine aminotransferase (ALT)/aspartate aminotransferase (AST) =\< to 2.5 times the upper limit of normal * Serum creatinine =\< to 1.6 mg/dl * Total bilirubin =\< to 1.5 mg/dl, except in patients with Gilbert's Syndrome who must have a total bilirubin less than 3.0 mg/dl Exclusion Criteria: * Women of child-bearing potential who are pregnant or breastfeeding because of the potentially dangerous effects of the treatment on the fetus or infant * Any form of primary immunodeficiency (such as severe combined immunodeficiency disease) * 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 * Concurrent opportunistic infections (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) * Concurrent systemic steroid therapy * History of severe immediate hypersensitivity reaction to any of the agents used in this study * History of coronary revascularization or ischemic symptoms * History of or active central nervous system (CNS) or peripheral nerve stimulation (PNS) involvement * Documented left ventricular ejection fraction (LVEF) of less than or equal to 45%; testing is required in patients with: * Clinically significant atrial and/or ventricular arrhythmias including but not limited to: atrial fibrillation, ventricular tachycardia, second or third degree heart block * Age \>= 60 years old * Pulmonary function testing in patients with: * A prolonged history of cigarette smoking (20 pk/yr of smoking within the past two years) * Symptoms of respiratory dysfunction