Binimetinib and Imatinib for Unresectable Stage III-IV KIT-Mutant Melanoma

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Have histologically or cytologically confirmed melanoma * Have unresectable Stage III or Stage IV melanoma, as per American Joint Committee on Cancer 8th edition guidelines, not amenable to local therapy * Have measurable disease by Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST v1.1) criteria * Have documentation of KIT-mutant melanoma by Clinical Laboratory Improvement Act (CLIA)-certified testing platform * Participants have progressed on prior standard-of-care therapy, or would be ineligible for or unable to tolerate standard-of-care therapy, in the opinion of the treating Investigator * For participants who have received prior ICI, the following is permitted: * Prior adjuvant or neoadjuvant ICI, if last dose administered at least 4 weeks prior to study drug start * Prior ICI for the treatment of unresectable/metastatic disease, if last dose administered at least 4 weeks prior to study drug start * Absolute neutrophil count \>= 1,500/microliter (mcL) * Platelets \>= 100,000/mcL * Total bilirubin below normal institutional limits, unless elevated due to Gilbert's syndrome and direct bilirubin is within normal limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase (SGOT)) =\< 3 x institutional upper limit of normal * Alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase (SGPT)) =\< 3 x institutional upper limit of normal * Creatinine =\< 1.5 x within institutional upper limit of normal OR creatinine clearance glomerular filtration rate (GFR) \>= 50 mL/min calculated using the Cockcroft-Gault formula * Human immunodeficiency virus (HIV)-infected individuals on effective anti-retroviral therapy, with undetectable viral load within 3 months of study drug start, are eligible for this trial * For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Individuals with a history of hepatitis C virus (HCV) infection must have been treated and cured. For individuals with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Individuals with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate central nervous system (CNS)-specific treatment is not required prior to study start * Individuals 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 for this trial * Imatinib and/or binimetinib may have teratogenic effects. Women of child-bearing potential (WOCBP) must agree to: * Use highly effective contraception to avoid pregnancy from screening through 30 days after the last dose of study drugs; * Refrain from donating ova during the study through 30 days after the end of systemic exposure to study drugs; * Inform her treating physician immediately should she become pregnant or suspect she is pregnant while she is participating in this study * Sexually active men enrolled on this protocol must agree to: * Use a condom for the duration of study participation and through 90 days after the end of systemic exposure to study drugs; * Refrain from donating sperm during the study through 90 days after the end of systemic exposure to study drugs; * If the male participant has a partner that is a WOCBP, that partner should also use highly effective contraception for the duration of the study and through 90 days after the end of the male participant's systemic exposure to study drug * Inform his treating physician immediately should his partner become pregnant while he is participating in this study Highly effective (i.e., failure rate \<1% per year when used consistently and correctly) methods of contraception include: * Complete abstinence from heterosexual intercourse * Combined (estrogen and progesterone) hormonal contraception associated with inhibition of ovulation (oral, intravaginal, transdermal) * Progesterone-only hormonal contraception associated with inhibition of ovulation (oral, injectable, implantable) * Intra-uterine device (IUD) * Intrauterine hormone-releasing system (IUS) * Bilateral tubal occlusion * Vasectomized male partner (provided the vasectomized male has received medical assessment of surgical success, and that the male is a female participant's sole sexual partner) * Ability to understand a written informed consent document, and the willingness to sign it * The participant is deemed by the Investigator to have the initiative and means to be compliant with scheduled visits, treatment plan, and study procedures Exclusion Criteria: * Has received systemic anti-cancer therapies within 3 weeks of study drug start, radiation within 2 weeks, antibody therapy within 4 weeks * Has not recovered from adverse events due to prior anti-cancer therapy to =\< grade 1 or baseline. Note: Stable chronic conditions (grade =\< 2) that are not expected to resolve (such as neuropathy, myalgia, alopecia, prior therapy-related endocrinopathies) are exceptions and may enroll * Is currently receiving any other investigational agents or has received an investigational agent within 14 days or within 5 half-lives of investigational agent (whichever is shorter), prior to start of study drugs * Inability to swallow and retain study drugs * Impairment of gastrointestinal function or disease which may significantly alter the absorption of study drugs (e.g., active ulcerative disease, uncontrolled vomiting or diarrhea, malabsorption syndrome, complete small bowel resection), or recent (=\< 3 months) history of a partial or complete bowel obstruction, or other conditions that will interfere significantly with the absorption of o