Uprosertib, Dabrafenib, and Trametinib in Treating Patients With Stage IIIC-IV Cancer

Inclusion Criteria: * PHASE I PORTION ELIGIBILITY CRITERIA: * Patients must have BRAF\^V600 mutant metastatic cancer irrespective of the histology or prior therapy; BRAF\^V600 mutant status must be documented by a Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory; use of an Food and Drug Administration (FDA)-approved test is preferred although other BRAF tests at a CLIA-certified laboratory may also be accepted * Patients must have locally advanced unresectable stage IIIC or metastatic stage IV cancer with either progression to prior therapy or a newly diagnosed cancer that does not have an available treatment with curative intent * Patients must have a complete physical examination and medical history within 28 days prior to registration * Patients must have measurable or non-measurable disease; all measurable lesions must be assessed (by physical examination, computed tomography \[CT\], or magnetic resonance imaging \[MRI\] scan) within 28 days prior to registration; tests to assess non-measurable disease must be performed within 42 days prior to registration; all disease must be assessed and documented on the baseline tumor assessment form (Response Evaluation Criteria in Solid Tumors \[RECIST\] 1.1) * All patients must undergo a CT or MRI of the brain within 42 days prior to registration; patients with asymptomatic brain metastases or previously treated brain metastases that are stable (i.e. not requiring corticosteroids) at the time of registration will be eligible * Patients may have received prior systemic therapy (chemotherapy, immunotherapy, biologic therapy, or combination regimens); all adverse events associated with prior treatment must have resolved to \< grade 1 prior to registration * Patients progressing on a prior BRAF inhibitor-based therapy will be eligible, as are patients naive to BRAF inhibitor therapy; resistance to BRAF inhibitor-based therapy will be defined as progressive disease by RECIST 1.1 criteria while receiving therapy with a BRAF inhibitor (vemurafenib or dabrafenib, alone or in combination with a mitogen-activated protein kinase \[MEK\] inhibitor); this may be innate resistance (patients who never achieved a tumor response while on BRAF inhibitor therapy) or acquired resistance (progression after having a tumor response to BRAF inhibitor therapy); there will not be a period of break between progression on the prior BRAF inhibitor-based therapy and the start of dabrafenib, trametinib and GSK2141795 * Patients may have received prior surgery (for both the primary and stage IV disease); all adverse events associated with prior surgery must have resolved to =\< grade 1 prior to registration * Patients may have received prior radiation therapy; all adverse events associated with prior radiation therapy must have resolved to =\< grade 1 prior to registration * Patients must be willing to submit blood for pharmacokinetics; sites must order S1221 pharmacokinetic (PK) kit immediately after registration; the Southwest Oncology Group (SWOG) patient identification (ID) number must be provided on the S1221 PK Kit request form * Patients must have available and be willing to submit baseline tissue taken at the time of disease progression to prior BRAF inhibitor-based therapy (either fresh frozen \[preferred\], or paraffin-embedded tumor blocks) OR must have a site of disease that can be biopsied within this study for translational medicine studies; tissue may be from an archival biopsy or a new biopsy after the patient has been registered to the protocol; since patients are referred to this protocol after progression on prior BRAF inhibitor-based therapy, the biopsy taken at the time of progression will be used as the baseline biopsy for this study; patients must be willing to submit plasma and whole blood for translational medicine studies * Patients must have Zubrod performance status =\< 1 * Absolute neutrophil count (ANC) \>= 1,200/ul (obtained within 28 days prior to registration) * Platelets \>= 100,000/ul (obtained within 28 days prior to registration) * Hemoglobin \>= 9 g/dL (obtained within 28 days prior to registration) * Total bilirubin =\< 1.5 x institutional upper limit of normal (IULN) (or =\< 2.5 x ULN for patients with Gilbert's syndrome) (with 28 days prior to registration) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x IULN (or \< 5 x IULN for patients with known liver metastases) (obtained within 28 days prior to registration) * Serum albumin \>= 2.5 g/dL (obtained within 28 days prior to registration) * Serum creatinine =\< 1.5 mg/dL OR measured or calculated creatinine clearance \>= 50 mL/min (obtained within 28 days prior to registration) * Patient must have a left ventricular ejection fraction \>= institutional lower limit of normal (LLN) by echocardiogram (ECHO) or multigated acquisition (MUGA) within 28 days prior to registration * Patients with melanoma must have a serum lactate dehydrogenase (LDH) test performed within 28 days prior to registration * Patients with human immunodeficiency virus (HIV) are eligible if they are not on antiviral agents and have adequate cluster of differentiation (CD)4 counts (\>= 500 mm\^3) * Patients receiving anticoagulation treatment are allowed to participate with international normalized ratio (INR) established within the therapeutic range * Women of childbearing potential must have a negative pregnancy test within 14 days of registration * Patients must be able to retain oral medication and must not have any clinically significant gastrointestinal abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach or bowels; patients who have feeding tubes can enroll in the study provided that the capsules do not need to be modified * Patients or their legally authorized representative must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines * As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system * Patients must be \>= 18 years of age * Patients must have a serum albumin \>= 2.5 g/dL within 28 days prior to registration * PHASE II PORTION ELIGIBILITY CRITERIA: * Patients must have histologically confirmed melanoma with BRAF\^V600 mutation; patients must have stage IIIC or stage IV disease * Patients must have received prior BRAF inhibitor therapy (e.g. dabrafenib, vemurafenib) within 56 days prior to registration; prior trametinib therapy is permitted; patients are not required to interrupt BRAF or MEK inhibitor therapy prior to the initiation of three agent combination therapy on study * Patients must have measurable disease; all measurable lesions must be assessed (by physical examination, CT, or MRI scan) within 28 days prior to registration; tests to assess non-measurable disease must be performed within 42 days prior to registration; patients whose only measurable disease is within a previous radiation therapy port must demonstrate clearly progressive disease (in the opinion of the treating investigator) prior to registration; all disease must be assessed and documented on the baseline tumor assessment form (RECIST 1.1) * Patients must have Zubrod performance status =\< 2 * No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease free for five years; patients with history of RAS mutation-positive tumors are not eligible regardless of interval from the current study; Note: Prospective RAS testing is not required; however, if the results of previous RAS testing are known, they must be used in assessing eligibility Exclusion Criteria: * Patients must not have a corrected QT (QTc) interval \>= 480 msecs within 28 days prior to registration * Patients must not have a history of acute coronary syndromes (including unstable angina), myocardial infarction within 6 months, coronary angioplasty, or stenting within the past 24 weeks; class II, III, or IV heart failure as defined by the New York Heart Association (NYHA) functional classification system; or history of known cardiac arrhythmias (such as atrial fibrillation) unless it has been stably controlled for \> 30 days prior to registration; abnormal cardiac valve morphology (\>= grade 2) documented by echocardiogram (subjects with grade 1 abnormalities \[i.e., mild regurgitation/stenosis\]) can be entered on study; subjects with moderate valvular thickening are not eligible * At the time of registration, patients must not be receiving any medications or substances that are strong inhibitors or inducers of cytochrome P450, family 3, subfamily A (CYP3A) or cytochrome P450, family 2, subfamily C, polypeptide 8 (CYP2C8); patients must not be planning to use herbal remedies (e.g., St. John's wort), or strong inhibitors or inducers of P-glycoprotein (Pgp) or breast cancer resistance protein 1 (Bcrp1) * Patients must not be pregnant or nursing due to unknown teratogenic side effects; women/men of reproductive potential must have agreed to use an effective contraceptive method; a woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months; in addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation; hormonal contraception is not allowed due to drug interactions which can render hormonal contraceptives ineffective; however, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures * Patient must not have uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, previously diagnosed type 1 diabetes mellitus/type 2 diabetes, psychiatric illness/social situations, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, that would limit compliance with study requirements; patients must not have any evidence of mucosal or internal bleeding; patients must not have a history of pneumonitis or interstitial lung disease; patients must not have received any major surgery within four weeks prior to registration * Patients must not have an active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection * Patients must not have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to dabrafenib or other agents used in this study including dimethyl sulfoxide (DMSO) * Patients with known history or current evidence of retinal vein occlusion (RVO) are not eligible: * History of RVO, or predisposing factors to RVO (e.g. uncontrolled glaucoma or ocular hypertension, uncontrolled systemic disease such as hypertension, diabetes mellitus, or history of hyperviscosity or hypercoagulability syndromes) * Visible retinal pathology as assessed by ophthalmic exam that is considered a risk factor for RVO such as: * Evidence of new optic disc cupping * Evidence of new visual field defects * Intraocular pressure \> 21 mmHg * NOTE: Ophthalmic exam is required for all patients; exam must be obtained within 28 days prior to registration * Patients must not have uncontrolled hypertension (defined as systolic blood pressure \> 140 mm Hg and/or diastolic blood pressure \> 90 mm Hg which cannot be controlled by anti-hypertensive therapy)