Genetically Modified Therapeutic Autologous Lymphocytes Followed by Aldesleukin in Treating Patients With Stage III or Metastatic Melanoma

Inclusion Criteria: * TURNSTILE I INCLUSION CRITERIA: * Patients must have metastatic melanoma or stage III in-transit, subcutaneous, or regional nodal disease (Turnstile I) * Patients must have a lesion amenable to resection for the generation of TIL (Turnstile I) * Patients must receive a magnetic resonance imaging (MRI)/computed tomography (CT)/positron emission tomography (PET) of the brain within 6 months of signing informed consent; if new lesions are present, patient must have definitive treatment; principal investigator (PI) or his designee should make final determination regarding enrollment (Turnstile I) * Clinical performance status of Eastern Cooperative Oncology Group (ECOG) 0-2 within 30 days of signing informed consent (Turnstile I) * Patients previously treated with immunotherapy, targeted therapy, or no therapy will be eligible; patients receiving cytotoxic agents will be evaluated by the PI or his designee * Patients with a negative pregnancy test (urine or serum) must be documented within 14 days of screening for women of childbearing potential (WOCBP); a WOCBP has not undergone a hysterectomy or who has not been naturally postmenopausal for at least 12 consecutive months (Turnstile I) * CHEMOTHERAPY/CELL INFUSION INCLUSION CRITERIA: * Patients must have adequate TIL available (Turnstile II) * Patients must have at least one biopsiable and measurable metastatic melanoma lesions \>= 1 cm (Turnstile II) * Patients may have brain lesions which measure =\< 1 c…