Trametinib With or Without GSK2141795 in Treating Patients With Metastatic Uveal Melanoma

Inclusion Criteria: * Patients must have metastatic histologically or cytologically confirmed uveal melanoma; if histologic or cytologic confirmation of the primary is not available, confirmation of the primary diagnosis of uveal melanoma by the treating investigator can be clinically obtained, as per standard practice for uveal melanoma; pathologic confirmation of metastatic disease will be performed at Memorial Sloan Kettering (MSK) or at a participating site * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan * Patients may not have received prior systemic or hepatic directed infusional/embolization therapies for advanced uveal melanoma; local therapies such as radiofrequency ablation or cryotherapy for metastatic disease are permitted but must have been performed at least 21 days prior to initiation of study therapy; lesions treated with local modalities such as radiofrequency ablation or cryotherapy may not be used as target lesions unless they demonstrate growth over a minimum of 3 months on subsequent imaging studies * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Life expectancy of greater than 3 months * Able to swallow and retain orally-administered medication and does not have any clinically significant gastrointestinal abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach or bowels * All prior treatment-related toxicities must be Common Terminology Criteria for Adverse Events (CTCAE) version (v)4 grade =\< 1 (except alopecia) at the time of randomization and crossover * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9.0 g/dL (not requiring transfusions within the past 2 weeks) * Total bilirubin =\< 1.5 x institutional upper limit of normal; Note: patients with hyperbilirubinemia clinically consistent with an inherited disorder of bilirubin metabolism (e.g., Gilbert syndrome) will be eligible at the discretion of the treating physician and/or the principal investigator * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 1.5 x institutional upper limit of normal for patients with no concurrent liver metastases, OR =\< 2.5 x institutional upper limit of normal for patients with concurrent liver metastases * Creatinine =\< 1.5 mg/dL OR calculated creatinine clearance (Cockcroft-Gault formula) \>= 50 mL/min OR 24-hour urine creatinine clearance \>= 50 mL/min * Left ventricular ejection fraction \>= institutional lower limit of normal (LLN) by echocardiogram (ECHO) or multigated acquisition scan (MUGA) * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; women of child-bearing potential must have a negative blood pregnancy test within 14 days prior to start of protocol treatment; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of trametinib administration * Ability to understand and the willingness to sign a written informed consent document * Patients must agree to provide all imaging studies for central radiology review; this central radiology review may be performed retrospectively and will not be utilized for decision making for patients on study * ELIGIBILITY CRITERIA FOR CROSSOVER REGISTRATION * Previously treated with trametinib on Arm A and experienced objective disease progression by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Not removed from trametinib treatment due to the development of unacceptable toxicity that is not manageable with dose reduction * No other drug treatment for malignant melanoma administered after completing study treatment with trametinib * Meet all eligibility criteria with the exception of: * Prior therapy with trametinib will be permitted * All laboratory parameters must be met as outlined except for ALT and total bilirubin, which must meet criteria for continued therapy * Patients who are eligible for cross-over will not need to undergo another ophthalmologic examination Exclusion Criteria: * History of another malignancy except for those who have been disease-free for 3 years, or patients with a history of completely resected non-melanoma skin cancer and/or patients with indolent secondary malignancies not requiring active therapy, are eligible; consult the study MSK Principal Investigator or the Cancer Therapy Evaluation Program (CTEP) Medical Monitor if unsure whether second malignancies meet the requirements specified above * History of interstitial lung disease or pneumonitis * Any major surgery or extensive radiotherapy within 21 days prior to randomization and crossover * Use of other investigational drugs within 28 days (or five half-lives, whichever is shorter; with a minimum of 14 days from the last dose) preceding the first dose of trametinib alone or with GSK2141795 and during the study * Symptomatic or untreated leptomeningeal or brain metastases or spinal cord compression; treated brain metastases must have been stable for at least 1 month * Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to trametinib, GSK2141795, or excipients or to dimethyl sulfoxide (DMSO) * Current use of a prohibited medication * History or current evidence/risk of retinal vein occlusion (RVO) or retinal pigment epithelial detachment (RPED) in the eye unaffected by uveal melanoma * Patients with abnormal fasting glucose values (values \> upper limit of normal \[ULN\] or \< LLN) at screening will be excluded; in addition, patients with type 1 diabetes will also be excluded; however, patients with type 2 diabetes will be allowed if diagnosed \>= 6 months prior to enrollment, and if presenting with a normal fasting glucose value and a regular hemoglobin A1C (HbA1C) =\< 8% at screening * History or evidence of cardiovascular risk including any of the following: * Left ventricular ejection fraction (LVEF) \< LLN * A QT interval corrected for heart rate using the Bazett's formula QTcB \>= 480 msec * History or evidence of current clinically significant uncontrolled arrhythmias (exception: patients with controlled atrial fibrillation for \> 30 days prior to randomization are eligible) * History of acute coronary syndromes (including myocardial infarction and unstable angina), coronary angioplasty, or stenting within 6 months prior to randomization * History or evidence of current \>= class II congestive heart failure as defined by the New York Heart Association (NYHA) functional classification system * Treatment-refractory hypertension defined as a blood pressure of systolic \> 140 mmHg and/or diastolic \> 90 mmHg which cannot be controlled by anti-hypertensive therapy * Patients with intra-cardiac defibrillators * Known cardiac metastases * Known hepatitis B virus (HBV) or hepatitis C virus (HCV) infection (patients with chronic or cleared HBV and HCV infection are eligible); patients with human immunodeficiency virus (HIV) are not eligible if on anti-retroviral medications * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * The study drug must not be administered to pregnant women or nursing mothers; women of childbearing potential should be advised to avoid pregnancy and use effective methods of contraception; men with a female partner of childbearing potential must have either had a prior vasectomy or agree to use effective contraception; if a female patient or a female partner of a patient becomes pregnant while the patient receives trametinib, the potential hazard to the fetus should be explained to the patient and partner (as applicable)