Molecularly Targeted Therapy in Treating Patients With BRAF Wild-type Melanoma That is Metastatic

Inclusion Criteria: * Patient with metastatic or locally advanced and unresectable BRAF wild-type melanoma who have either progressed following previous treatment of immunotherapy, or are not eligible for immunotherapy; pts. are defined as "BRAF wild-type" if they test negative for V600 mutations based on a Clinical Laboratory Improvement Amendments (CLIA) certified assay * Patients must have tumor accessible by interventional radiology or surgical intervention and suitable for biopsy (BX) with 5-6 passes of a 16 or 18 gauge needle for core BX (defined as at least 1 cm\^3 tumor/50 mg accessible for BX), and must agree to undergo up to two surgical resections/biopsies to collect tumor for research purposes; the first of these biopsies will occur at the beginning of the study, prior to genetic analysis and Rx; the second BX will be performed at the time of DZ progression/end of study should funding be available * Patients must have measurable DZ (per Response Evaluation Criteria in Solid Tumors \[RECIST\] version 1.1 \[v1.1\] criteria), defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or a subcutaneous or superficial lesion that can be measured with calipers by clinical exam; for lymph nodes, the short axis must be \>= 15 mm * Previous therapies: prior radiation therapies, immunotherapies, and investigational therapies are allowed as follows. * Radiation: prior radiation therapy (RT) is allowed with the following conditions: * Patients who have received minimal RT (=\< 5% of their total marrow volume) must have completed it \>= 2 weeks prior to the initiation of study Rx * Patients who have received RT that constituted \> 5% but \< 50% of their total marrow volume must have completed it \>= 4 weeks prior to the initiation of study treatment * Patients who have received prior radiation to 50% or more of their total marrow volume will be excluded * Patients may be biopsied while undergoing RT as long as BX site is not in the radiation portal; however, they still have to wait the required amount of time from radiation to treatment even though the tumor board may have already occurred and a treatment plan assigned * Other therapies: prior investigational or targeted therapies and immunotherapies may be allowed following discussion with the PI (PI); if the PI deems the prior treatment acceptable, patients must not have received these therapies for 28 days or five half-lives of the drug (whichever is lesser) prior to the initiation of study treatment and must have full recovery from any acute effects of these therapies; prior therapy with mitogen-activated protein kinase (MEK) inhibitors will not be allowed * Patients with chronic grade 2 toxicity may be eligible at the discretion of the PI if the condition has been stable, and not worsening, for at least 30 days; pts. with ongoing alopecia of any grade will be eligible * Patient must have a life expectancy of \>= 3 months, as estimated by the treating oncologist * Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Hemoglobin \>= 9 g/dL * Leukocytes \>= 3,000/microliter (mcL) * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelets (PLT) \>= 100,000/mcL * Aspartate aminotransferase (AST) =\< 2.5 x upper limit of normal (ULN); if liver metastases are present, =\< 5 x ULN * Alanine aminotransferase (ALT) =\< 2.5 x ULN; if liver metastases are present, =\< 5 x ULN * Bilirubin =\< 1.5 x ULN * Creatinine =\< 1.5 x ULN OR calculated or measured creatinine clearance \>= 50 mL/min/1.73 m\^2 for pts. with creatinine above institutional normal * If available, pt. must agree to provide archival tissue for research purposes (either archival paraffin tissue block or 10 unstained slides of a primary or metastatic melanoma lesion) prior to enrollment; samples should be shipped within 1 month after enrollment * Patient agrees to having a blood sample (a minimum of 10 mL, with 20 mL preferred) drawn and analyzed to compare their normal genetic profile to that of their tumor sample * Patient must be able to tolerate oral medication * Women of child-bearing potential and men must agree to use 2 forms of adequate contraception (hormonal or barrier method of birth control; abstinence) for the duration of study participation, and for four months following completion of study therapy; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately; women who become pregnant must immediately discontinue Rx with any study therapy; male pts. should avoid impregnating a female partner; male pts., even if surgically sterilized, (i.e. post-vasectomy) must agree to one of the following: practice effective barrier contraception during the entire study Rx period and through 4 months after the last dose of study drug, or completely abstain from sexual intercourse * Patient must have the ability to understand and the willingness to sign a written informed consent document * Patient must be willing and able to comply with the protocol for the duration of the study, including attending scheduled visits, examinations, the BX procedure, and having their tumor and blood molecularly characterized * Patient understands they must meet all inclusion and exclusion criteria in the drug specific appendix for which they were assigned. Exclusion Criteria: * Patients with peripheral neuropathy \>= grade 2 are not permitted unless discussed with the PI and only in unique circumstances (i.e. unilateral neuropathy due to trauma) * Patient has DZ that tests positive for BRAF V600 mutations based on the results of a CLIA certified assay * Patients with active infection at time of BX * Patients with any evidence of severe or uncontrolled systemic DZ(s) including known cases of hepatitis B or C or human immunodeficiency virus (HIV); screening for chronic conditions is not required, although pts. known to have such conditions at screening should not be included * Any patient requiring chronic maintenance of red blood cell, white blood cell or granulocyte counts through the use of blood transfusions or growth factor support (e.g. Neulasta®, Neupogen®) * Patients with a prior history of seizures within the past year unrelated to brain metastases * Patients with known active progressive brain metastases; pts. with prior treated brain metastases are allowed, providing that they were not accompanied by seizures within the past year and that a baseline brain MRI scan prior to study entry demonstrates no current evidence of active brain metastases; all pts. with prior treated brain metastases must be stable for \> 1 months after treatment and off steroid treatment prior to study enrollment * Patients receiving any other anti-cancer therapy (cytotoxic, biologic, radiation, or hormonal other than for replacement) except for medications that are prescribed for supportive care but may potentially have an anti-cancer effect (i.e. megestrol acetate, bisphosphonates); these medications must have been started \>= month prior to enrollment on this study; pts. may be on low molecular weight heparin or direct factor Xa inhibitors * Patients with any clinically significant medical condition which, in the opinion of the investigator, makes it undesirable for the pt. to participate in the study or which could jeopardize compliance with protocol requirements including, but not limited to: ongoing or active infection, significant uncontrolled hypertension, or severe psychiatric illness/social situations * Patients with preexisting cardiac conditions, including uncontrolled or symptomatic angina, arrhythmias, or congestive heart failure will not be eligible * Patients with left ventricular ejection fraction (LVEF) \< 45% will not be eligible * Patients with either of the following within 6 months before the first dose of study treatment: * Stroke (including transient ischemic attack \[TIA\], or other ischemic event) * Myocardial infarction * Patients with acute gastrointestinal bleeding within 1 month of study entry * Patients who have, at screening, corrected QT interval using Fridericia's formula (QTcF) \>= 450 msec for males and QTcF \>= 470 for females * Patients with a co-morbid condition(s) that, in the opinion of the investigator, prevents safe surgery/BX procedure * Patients with malabsorption syndrome or other condition that would interfere with intestinal absorption or ability to swallow oral medication * Pregnant or nursing women; breastfeeding must be discontinued prior to Rx * Patients who have received organ transplant * Patients who have had major surgery within 14 days of study enrollment * Patients diagnosed or treated for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, or an in situ malignancy. Patients with a low grade prostate cancer, not on hormonal therapy, for which the disease is confined to the prostate may be considered eligible by the overall Principal Investigator on a case by case basis.