Nivolumab and Ipilimumab in Treating Patients With Metastatic Uveal Melanoma

Inclusion Criteria: * Willing and able to give written informed consent * History of uveal melanoma and documented metastatic disease with at least one measurable lesion is required; which is \>= 1 cm x 1 cm (on spiral computed tomography \[CT\] or equivalent) * Any number of prior therapies is allowed * White blood cell (WBC) \>= 2000/uL * Absolute neutrophil count (ANC) \>= 1500/uL * Platelets \>= 100 x 10\^3/uL * Hemoglobin \>= 9 g/dL * Creatinine =\< 1.5 x upper limit of normal (ULN) or creatinine clearance (CrCl) \> 40 mL/min (using the Cockcroft-Gault formula) * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3 x ULN for patients without liver metastasis, =\< 5 x ULN for liver metastases * Bilirubin =\< 1.5 x ULN, (except patients with Gilbert's syndrome, who must have a total bilirubin less than 3.0 mg/dL) * In suspected patients no active or chronic infection with human immunodeficiency virus (HIV), hepatitis B, or hepatitis C * Performance status Eastern Cooperative Oncology Group (ECOG) 0-1 * Baseline imaging in the form of CT chest, abdomen, pelvis with oral and intravenous contrast within 28 days of study entry; for patients with a contrast allergy, choice of alternative body imaging will be at the discretion of the investigator or his designee; magnetic resonance imaging (MRI) of the brain is only needed if clinically indicated * Prior to start of treatment must be more than 21 days elapsed from surgery, radiation therapy, or prior chemothera…