Therapeutic Autologous Lymphocytes, Aldesleukin, and Denileukin Diftitox in Treating Patients With Stage III-IV Melanoma

Inclusion Criteria: * Histopathological documentation of melanoma * Expression of human leukocyte antigen (HLA)-A2 or B44 as determined by HLA typing lab * Patients whose tumor expresses targeted antigen and restricting allele against which CD8 T cell clones can be generated * Karnofsky Performance status of at least 80% and an expected survival of greater than 6 months * Bi-dimensionally measurable disease by palpation on clinical exam, or radiographic imaging (X-ray, computed tomography \[CT\] scan) * Normal cardiac stress test (treadmill, echocardiogram, or myocardial perfusion scan) within 182 days prior to enrollment is required of patients with a history of cardiac disease * Pulse \> 45 or \< 120 * Weight \>= 45 kg * Temperature =\< 38C (\< 100.4 F) * White blood cells (WBC) \>= 3,000 * Hematocrit (HCT) \>= 30% * Platelets \>= 100,000 * Patients must be willing and able to discontinue the use of all antihypertensive medications 24 hours prior to and during IL2 therapy Exclusion Criteria: * Pregnant women, nursing mothers, or women of reproductive ability who are unwilling to use effective contraception or abstinence * Serum creatinine \> 1.6mg/dL * Creatinine clearance \< 75 ml/min * Aspartate aminotransferase (AST) \> 2.5 x upper limit of normal * Alanine aminotransferase (ALT) \> 2.5 x upper limit of normal * Bilirubin \> 1.6 or international normalized ratio (INR) \> 1.5 due to hepatic dysfunction * Albumin \< 3.0g/dL * Clinically significant pulmonary dysfunction, as determined by medical history and physical exam; patients so identified will undergo pulmonary functions testing and those with Forced expiratory volume in one second (FEV1) \< 80% predicted or diffusing capacity of the lung for carbon monoxide (DLco) (corr for hemoglobin \[Hgb\]) \< 75% will be excluded * Significant cardiovascular abnormalities as defined by any one of the following: congestive heart failure, symptoms of coronary artery disease * Symptomatic central nervous system (CNS) metastases greater than 1 cm at time of therapy; patients with 1-2 asymptomatic, less than 1cm brain/CNS metastases without significant edema may be considered for treatment * Patients with active infections or oral temperature \> 38.2 C within 48 hours of study entry or systemic infection requiring chronic maintenance or suppressive therapy * Chemotherapeutic agents (standard or experimental), radiation therapy, or other immunosuppressive therapies less than 3 weeks prior to T cell therapy) * Concurrent treatment with steroids * Patients must not be receiving any other experimental drugs within 3 weeks of the initiation of the protocol and must have recovered from all side effects of such therapy * The following agents are not allowed while on study: systemic corticosteroids (except as outlined for management of toxicity of nontransduced CTL), immunotherapy (for example, interleukins, interferons, melanoma vaccines, intravenous immunoglobulin, expanded polyclonal TIL or LAK therapy), pentoxifylline, or other investigational agents