Ipilimumab With Lymphodepletion Plus Adoptive Cell Transfer and High Dose IL-2 in Melanoma Mets Pts

Inclusion Criteria: * Participants must have unresectable metastatic stage IV melanoma or stage III intransit or regional nodal disease, and in the opinion of the institutional PI is an acceptable candidate for ACT with high dose IL-2 * Residual measurable disease after resection of target lesion(s) for TIL growth * Tumor may have a B-RAF V600 mutation or be BRAF wild type, and patients must not have been previously treated with ipilimumab * Clinical performance status of Eastern Cooperative Oncology Group (ECOG) 0 - 1. ECOG performance status of 0-1 will be inferred if the patient's level of energy is ≥ 50% of baseline. * May have been previously treated for metastatic disease, or may have not had prior systemic treatment. Patients with a V600 BRAF mutated tumor may have previously received a prior BRAF inhibitor. * Women of childbearing potential (WOCBP) must have a negative serum pregnancy test within 7 days of screening. * Adequate renal, hepatic and hematologic function, including creatinine of less than or equal to 1.7 gm/dL, total bilirubin less than or equal to 2.0 mg/dL, except in patients with Gilbert's Syndrome who must have a total bilirubin less than 3.0 mg/dL, aspartate aminotransferase (AST) and alanine transaminase (ALT) of less than 3 X institutional upper limit of normal, hemoglobin of 8 gm/dL or more, white blood count (WBC) of 3000 per mcL and total granulocytes of 1000 per mcL or more, and platelets of 100,000 per mcL or more. * Must have a positive screening Epstein-Barr virus (EBV) antibody titre on screening test * Potential participants with antibiotic allergies per se are not excluded; although the production of TIL for adoptive transfer includes antibiotics, extensive washing after harvest will minimize systemic exposure to antibiotics. * At screening, patients with ≤ 3 untreated CNS metastases may be included provided none of the untreated lesions are \> 1 cm in greatest dimension, and there is no peri-tumoral edema present on brain imaging (MRI or CT if MRI is contraindicated). * At screening, patients with central nervous system (CNS) metastases treated with either surgical resection and/or radiation therapy may be included. Patients may be included if the largest lesion is ≤ 1 cm, and there is no evidence of progressive CNS disease on brain imaging at least 28 days after treatment. * At screening, patients may be included if the largest lesion is \> 1 cm or \> 3 in number, and there is no evidence of progressive CNS disease on brain imaging at least 90 days after treatment with surgery and/or radiation therapy. * No evidence of ongoing cardiac dysrhythmia ≥ grade 2 (NCI Common Terminology Criteria for Adverse Events \[CTCAE\], v4.0) * All laboratory and imaging studies must be completed and satisfactory within 30 days of signing the consent document, with the exceptions of: negative serum pregnancy test for women of child-bearing potential which must be negative within 7 days of screening, human leukocyte antigen (HLA) typing which will not be repeated if performed previously, and pulmonary function tests (PFTs)/cardiac stress tests whose results are valid for 6 months if performed previously. Exclusion Criteria: * Active systemic infections requiring intravenous antibiotics, coagulation disorders or other major medical illness of the cardiovascular, respiratory or immune system, which in the opinion of the principal investigator (PI) or treating coinvestigator is not acceptable risk for ACT, are excluded. * Testing positive for HIV titre, Hepatitis B surface antigen, Hepatitis B core antibody, Hepatitis C antibody, Human T-Lymphotropic Virus (HTLV) I or II antibody, or both Rapid. Plasma Reagin (RPR) and fluorescent treponemal antibodies (FTA) positive are excluded. * Pregnant or nursing * Patients needing chronic, immunosuppressive systemic steroids are excluded * History of autoimmune disease that require immunosuppressive medications at the time of screening * Presence of a significant psychiatric disease, which in the opinion of the principal investigator or his designee, would prevent adequate informed consent or render immunotherapy unsafe or contraindicated * Patients with \> 3 untreated CNS metastases or evidence of peri-tumoral edema * Patients with ≤ 3 untreated CNS metastases but with at least one lesion \>1 cm or peri-tumoral edema * Patients with invasive malignancy other than melanoma at the time of enrollment and within 2 years prior to the first TIL administration are excluded, except for adequately treated (with curative intent) basal or squamous cell carcinoma, in situ carcinoma of the cervix, in situ ductal adenocarcinoma of the breast, in situ prostate cancer, or limited stage bladder cancer or other cancers from which the patient has been disease-free for at least 2 years. * Patients with treated CNS metastases \> 1 cm or \> 3 in number will be excluded if there is evidence of progressive CNS disease on brain imaging at least 90 days after treatment with surgery and/or radiation therapy. * Unable to comprehend and give informed consent * Male patients with WOCBP partners who do not agree to use two FDA-accepted forms of contraception during sexual intercourse with women of child-bearing potential from the start of ipilimumab and up to at least 6 months after ACT * WOCBP who do not agree to use 2 FDA forms of contraception during sexual intercourse from the start of ipilimumab and up to at least 6 months after ACT * Patients who have received ipilimumab in the past