Testing the Safety and Effectiveness of Combining Two Drugs, PLX2853 and Trametinib in the Treatment of Advanced Uveal Melanoma

Inclusion Criteria: * Patients must have histologically documented advanced uveal melanoma. Pathology review and confirmation of diagnosis will occur at the site enrolling the patient on this study. Patients must have locally advanced unresectable or metastatic uveal melanoma (UM). * Patients must have at least one lesion which is measurable according to Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 criteria. Measurable disease is not required in the phase I portion * Patients may be treatment-naïve or have received any number of prior systemic or liver-directed therapies for advanced UM. There are no maximum number of prior therapies received * There is no specified washout time for prior therapies however patients must have fully recovered from acute toxicities related to prior anti-cancer therapies including \* Cytotoxic therapies, immunotherapy, small molecule targeted agents, cell therapy, liver-directed therapy, or radiation therapy * Not pregnant and not nursing, because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown. Therefore, for women of childbearing potential only, a negative pregnancy test done =\< 7 days prior to registration is required * Age \>= 18 years * Eastern Cooperative Oncology Group (ECOG) Performance Status 0-2 * Absolute neutrophil count (ANC) \>= 1000/mm\^3 * Hemoglobin \>= 9g/dL (transfusions to achieve this level are allowed) * Platelet count \>= 100,000/mm\^3 * Creatinine clearance \>= 45 mL/minute (per Cockcroft-Gault equation) * Total bilirubin =\<1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) / alanine aminotransferase (ALT) =\< 3 x upper limit of normal (ULN) * Prothrombin time (PT)/international normalized ratio (INR) =\< 1.5 x upper limit of normal (ULN) * No history of any medical condition such as uncontrolled infection (including hepatitis B \[HepB\], hepatitis C \[HepC\]), uncontrolled diabetes mellitus or cardiac disease which, in the opinion of the treating physician, would make this protocol unreasonably hazardous for the patient * Patients who are human immunodeficiency virus (HIV)-infected on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible * Patients with a new or progressive brain metastases (active brain metastases) or leptomeningeal disease if the treating physician determines that immediate central nervous system (CNS) specific treatment is not required and is unlikely to be required during the first cycle of therapy are eligible * Patients with a known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification with a class 2B or better are eligible * Patients must be able to obtain confirmation of payment coverage (insurance or other) for trametinib \* Trametinib will not be provided by the Alliance and must be obtained through commercial or other mechanisms independent of the clinical trial. Confirmation of payment coverage or medication access must be obtained by treating physician prior to registration Exclusion Criteria * Patients must not have received prior treatment with a BET or MEK inhibitor * No patients who cannot swallow oral formulations of the agent(s) * Chronic concomitant treatment with strong inhibitors of CYP3A4 is not allowed on this study. Patients on strong CYP3A4 inhibitors must discontinue the drug for 14 days prior to registration on the study