Autologous CD8+ SLC45A2-Specific T Lymphocytes With Cyclophosphamide, Aldesleukin, and Ipilimumab in Treating Patients With Metastatic Uveal Melanoma

Inclusion Criteria:

* PHERESIS (TURNSTILE 1): Histopathologic documentation of melanoma concurrent with the diagnosis of metastatic disease or high-risk primary uveal melanoma defined as a recurrence score of \> 50% in 5 years. A diagnosis of uveal melanoma can be made clinically without primary tissue evaluation, based on history and records. A prior history of brachytherapy to the eye is sufficient clinical support for a diagnosis of uveal melanoma.
* PHERESIS (TURNSTILE 1): Hematocrit (HCT) \>= 24% or hemoglobin (HB) \>= 8 g/dL.
* PHERESIS (TURNSTILE 1): Platelets \> 50,000.
* PHERESIS (TURNSTILE 1): Expression of human leukocyte antigen (HLA)-A:0201 or HLA-A:2402.
* PHERESIS (TURNSTILE 1): Eastern Cooperative Oncology Group (ECOG)/ Zubrod performance status of 0-1.
* PHERESIS (TURNSTILE 1): Women of childbearing potential (WOCBP) must be using an adequate method of contraception to avoid pregnancy throughout the study in such a manner that the risk of pregnancy is minimized. Suggested precautions should be used to minimize the risk or pregnancy for at least 1 month before start of therapy, and while women are on study for up to 3 months after completion of the study. WOCBP include any female who has experienced menarche and who has not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation or bilateral oophorectomy) or is not postmenopausal.
* PHERESIS (TURNSTILE 1): Male patients must be willing and able to use an acceptable method of birth control, during and for at least 3 months after completion of the study, if their sexual partners are WOCBP.
* PHERESIS (TURNSTILE 1): Willing and able to give informed consent.
* PHERESIS (TURNSTILE 1): Toxicity related to prior therapy must either have returned to =\< grade 1, baseline, or been deemed irreversible. Certain non-serious exceptions include alopecia, hypothyroidism, neuropathy, nausea, adrenocortical deficiency requiring physiologic replacement dose of steroids, and other conditions noted and approved by the principal investigator (PI).
* T CELL INFUSION (INCLUDES CYCLOPHOSPHAMIDE, T CELL, ANTI-CTLA4 INFUSIONS AND SC IL-2) (TURNSTILE 2): ECOG/Zubrod performance status of 0-1 (evaluate at least 1 week before T cell infusion).
* T CELL INFUSION (INCLUDES CYCLOPHOSPHAMIDE, T CELL, ANTI-CTLA4 INFUSIONS AND SC IL-2) (TURNSTILE 2): Bi-dimensionally measurable disease by palpation on clinical exam, or radiographic imaging per irRC (evaluate at least 1 week before T cell infusion).
* T CELL INFUSION (INCLUDES CYCLOPHOSPHAMIDE, T CELL, ANTI-CTLA4 INFUSIONS AND SC IL-2) (TURNSTILE 2): At least 4 weeks must have elapsed since the last chemotherapy, targeted therapy, immunotherapy, radiotherapy, liver-directed therapy, or major surgery. At least 6 weeks for nitrosoureas, mitomycin C and liposomal doxorubicin. If started before T-cell administration, ipilimumab infusions must be least 21 days apart (evaluate at least 1 week before T cell infusion).
* T CELL INFUSION (INCLUDES CYCLOPHOSPHAMIDE, T CELL, ANTI-CTLA4 INFUSIONS AND SC IL-2) (TURNSTILE 2): For the ipilimumab cohort only: Toxicity related to prior therapy must either have returned to =\< grade 1, baseline, or been deemed irreversible. Certain non-serious exceptions include alopecia, hypothyroidism, neuropathy, nausea, adrenocortical deficiency requiring physiologic replacement dose of steroids, and other conditions noted and approved by the PI (evaluate at least 1 week before T cell infusion).
* T CELL INFUSION (INCLUDES CYCLOPHOSPHAMIDE, T CELL, ANTI-CTLA4 INFUSIONS AND SC IL-2) (TURNSTILE 2): Patients must have liver metastasis (evaluate at least 1 week before T cell infusion).
* T CELL INFUSION (INCLUDES CYCLOPHOSPHAMIDE, T CELL, ANTI-CTLA4 INFUSIONS AND SC IL-2) (TURNSTILE 2): Persons of reproductive potential must agree to use and utilize an adequate method of contraception throughout treatment and for at least 3 months after completion of study (evaluate at least 1 week before T cell infusion).
* T CELL INFUSION (INCLUDES CYCLOPHOSPHAMIDE, T CELL, ANTI-CTLA4 INFUSIONS AND SC IL-2) (TURNSTILE 2): Willing and able to give informed consent (evaluate at least 1 week before T cell infusion).

Exclusion Criteria:

* PHERESIS: Secondary malignancy is allowed providing it does not require concurrent therapy.
* PHERESIS: Pregnant women, nursing mothers, men or women of reproductive ability who are unwilling to use effective contraception. Women of childbearing potential with a positive pregnancy test within 3 days prior to pheresis.
* PHERESIS: Significant cardiovascular abnormalities as defined by any one of the following:

  * Congestive heart failure
  * Clinically significant hypotension
  * Symptoms of coronary artery disease (angina, dyspnea)
  * Presence of cardiac arrhythmias on electrocardiogram (EKG) requiring drug therapy
* PHERESIS: Autoimmune disease: Patients with a history of inflammatory bowel disease are excluded from this study, as are patients with a history of autoimmune disease (e.g. systemic lupus erythematosus, vasculitis, infiltrating lung disease) whose possible progression during treatment would be considered by the investigator to be unacceptable. Acceptable exclusions include: Hashimoto's thyroiditis, type 1 diabetes mellitus, and other localized or inactive conditions with approval of the PI.
* PHERESIS: Any underlying medical or psychiatric condition, which in the opinion of the investigator, will make the administration of study drug hazardous or obscure the interpretation of adverse events, such as a condition associated with frequent diarrhea.
* PHERESIS: Positive screening tests for human immunodeficiency virus (HIV), hepatitis B virus (Hep B), and hepatitis C virus (Hep C). If positive results are not indicative of true active or chronic infection, the patient can be treated.
* PHERESIS: Participation in any other immunotherapy treatment, that in the opinion of the principal investigator would be unsafe to receive further checkpoint blockade immunotherapy
* White blood cell (WBC) =\< 2000/uL (prior to cyclophosphamide and T cell infusions).
* Hct =\< 24% or Hb =\< 8 g/dL (prior to cyclophosphamide and T cell infusions).
* Absolute neutrophil count (ANC) =\< 1000 (prior to cyclophosphamide and T cell infusions).
* Platelets =\< 50,000 (prior to cyclophosphamide and T cell infusions).
* Creatinine \>= 3.0 x upper limit of normal (ULN) (prior to cyclophosphamide and T cell infusions).
* Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) \>= 5 x ULN (since all patients will have liver metastasis) (prior to cyclophosphamide and T cell infusions).
* Bilirubin \>= 3 x ULN (prior to cyclophosphamide and T cell infusions).
* Pregnant women, nursing mothers, men or women of reproductive ability who are unwilling to use effective contraception. Women of childbearing potential with a positive pregnancy test within 3 days prior to entry.
* 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) \< 2.0 L or diffusing capacity of the lung for carbon monoxide (DLCO) (corrected \[corr\] for hemoglobin \[Hgb\]) \< 50% will be excluded.
* Steroids (at prednisone equivalent doses \> 10 mg) are not permitted 3 days prior to T cell infusion and concurrently during therapy. Exceptions include use of systemic prednisone equivalent doses =\< 10 mg/ day, topical steroids or physiologic replacement dose of steroids for adrenocortical deficiency.
* Any non-oncology vaccine therapy used for the prevention of infectious disease within 1 month before or after any ipilimumab dose.
* Patients may not be on any other treatments for their cancer aside from those included in the protocol. Patients may not undergo another form of treatment concurrently with this study. Oncology supportive treatments such as growth factors, bone modifying agents, pain or nausea management are allowed.