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 gastrointe…