Ipilimumab and Nivolumab With Immunoembolization in Treating Participants With Metastatic Uveal Melanoma in the Liver

Inclusion Criteria: * Histologically confirmed metastatic uveal melanoma in the liver; patients must have at least one measurable liver metastasis that is \>= 10 mm in longest diameter by computed tomography (CT) scan or magnetic resonance imaging (MRI) * The total volume of the tumors must be less than 50% of the liver volume * Willingness and ability to give informed consent * Agreement to access archival tissue or agreement for tumor biopsy prior to treatment * Eastern Cooperative Oncology Group (ECOG) performance status of 0, or 1 * Serum creatinine =\< 2.0 mg/dl * Granulocyte count \>= 1000/mm\^3 * Platelet count \>= 100,000/mm\^3 * Bilirubin =\< 2.0 mg/ml * Albumin \>= 3.0 g/dl * Prothrombin time (PT)/partial thromboplastin time (PTT) less than 1.5 times normal * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) less than 3 x upper limit of normal (ULN) * Alkaline phosphatase less than 1.5 times ULN (grade 1) * Women must not be pregnant or breast-feeding * Women of child-bearing potential must use at least two other accepted and effective methods of contraception and/or to abstain from sexual intercourse for at least 23 weeks after the last dose of nivolumab and/or ipilimumab and sexually active males must use at least two other accepted and effective methods of contraception and/or to abstain from sexual intercourse for at least 31 weeks after the last dose of nivolumab and/or ipilimumab Exclusion Criteria: * Failure to meet any of the criteria set forth in the inclusion criteria section * Previous systemic exposure to anti-CTLA-4 antibody or anti-PD1 antibody * Previous liver-directed treatments including chemoembolization, radiosphere, hepatic arterial perfusion, or drug-eluting beads; liver resection and focal ablation are permitted * Presence of symptomatic liver failure including ascites and hepatic encephalopathy * Presence of untreated brain metastases; if patients have had previous treatment for the brain metastasis, an MRI or CT scan of the brain must confirm the stabilization of the brain metastasis for more than 2 months * Presence of uncontrolled hypertension or congestive heart failure, or acute myocardial infarction within 6 months of entry * Presence of any other medical complication that implies survival of less than six months * Uncontrolled severe bleeding tendency or active gastrointestinal (GI) bleeding * Significant allergic reaction to contrast dye or granulocyte-macrophage colony-stimulating (GM-CSF) * Immunosuppressive treatments within 4 weeks prior to embolization, unless prednisone =\< 5 mg or equivalent * Pregnancy or breast-feeding women * Patients with active hepatitis with serum glutamic-oxaloacetic transaminase (SGOT) and serum glutamate pyruvate transaminase (SGPT) equal or greater than 5 times normal * Biliary obstruction, biliary stent or prior biliary surgery except cholecystectomy * Positive for known human immunodeficiency virus (HIV) Infection * Uncontrolled chronic obstructive pulmonary disease or previous known pulmonary fibrosis * Active infection * Auto-immune disease including inflammatory bowel disease, lupus, rheumatoid arthritis, but not including hypothyroidism or psoriasis if condition has been stable for 2 months or greater