Pembrolizumab and Imatinib in Patients With Locally Advanced/Metastatic Melanoma With c-KIT Mutation/Amplification

Inclusion Criteria: * Patient must have histologically or cytologically confirmed diagnosis of stage III melanoma inoperable/not amenable to local treatment or stage IV melanoma. * Patient must have either mutation or amplification of c-KIT gene tested by commercially available molecular or gene sequencing techniques * Be willing and able to provide written informed consent/assent for the trial * Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Be willing to provide tissue from a newly obtained core or excisional biopsy of a tumor lesion; newly-obtained is defined as a specimen obtained up to 6 weeks (42 days) prior to initiation of treatment on day 1; subjects for whom newly-obtained samples cannot be provided (e.g. inaccessible or subject safety concern) may submit an archived specimen only upon agreement from the sponsor * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale * Absolute neutrophil count (ANC) \>= 1,500 /mcL * Platelets \>= 100,000 / mcL * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment) * Serum creatinine =\< 1.5 X upper limit of normal (ULN) or measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN * Serum total bilirubin =\< 1.5 X ULN or direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X ULN OR =\< 5 X ULN for subjects with liver metastases * Albumin \>= 2.5 mg/dL * International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants * Activated Partial Thromboplastin Time (aPTT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Female subject of childbearing potential must have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female subjects of childbearing potential must be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication; subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year * Male subjects must agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy Exclusion Criteria: * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment * Has a diagnosis of immunodeficiency or is receiving immunosuppressive therapy within 7 days prior to the first dose of trial treatment; individuals who are receiving systemic steroid therapy at a stable dose less than or equal to 10mg of prednisone per day or its equivalent will be permitted to participate * Has a known history of active TB (bacillus tuberculosis) * Hypersensitivity to pembrolizumab, imatinib, or any of its excipients * Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent * Note: subjects with =\< grade 2 neuropathy and/or alopecia are an exception to this criterion and may qualify for the study * Note: if subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Has a known additional malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids at a dose exceeding 10mg of prednisone per day or its equivalent for at least 7 days prior to trial treatment; this exception does not include carcinomatous meningitis, which is excluded regardless of clinical stability * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids exceeding 10 mg prednisone per day or its equivalent, or immunosuppressive drugs); replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Has known history of, or any evidence of, active, non-infectious pneumonitis * Has an active infection requiring systemic therapy * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has decompensated congestive heart failure as defined by New York Heart Association (NYHA) functional classification III or IV * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment * Has received prior therapy with an anti-programmed cell death (PD)-1, anti-PD-L1, or anti-PD-L2 agent * Has received prior therapy with imatinib or another tyrosine kinase inhibitor * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * Has received a live vaccine within 30 days of planned start of study therapy * Note: seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines, and are not allowed