A Study of MEK162 (Binimetinib) in Combination With Pexidartinib in Patients With Advanced Gastrointestinal Stromal Tumor (GIST)

Inclusion Criteria: * Patients must have pathologically confirmed GIST. * In the Phase I dose escalation study, must have locally advanced, unresectable or metastatic GIST and have progressed on imatinib. * In the dose expansion portion of the phase I study, patients must have locally advanced, unresectable or metastatic GIST that is resistant to imatinib. This population includes patients who have not been treated with imatinib (imatinib-naïve) but considered to have primary resistance to imatinib, i.e. KIT/PDGFRA wild-type GIST, and patients with imatinib-refractory disease, i.e. has had prior treatment with imatinib. * Patients must be at least 18 years of age. * Disease must be measurable by RECIST 1.1. * ECOG Performance Status 0 or 1. * Patient must be able to take oral medications. * Patients must sign an informed consent document. * Adequate renal, hepatic, and hematologic function defined by: * Serum Creatinine ≤ 1.5 mg/dL * Total Serum Bilirubin ≤ 1.5 x upper limit of normal (ULN) * Serum AST (SGOT) and/or ALT (SGPT) ≤ 2.5 x ULN (or ≤ 5.0 x ULN if considered due to tumor) * ANC ≥ 1500/mm\^3 * Platelets ≥ 100,000/mm\^3 * Hemoglobin ≥ 9g/dL * Patients of childbearing potential are permitted in the study so long as they consent to avoid getting their partner pregnant or becoming pregnant, respectively, by using a reliable methods of contraception during and for 3 months following the last dose of the study drugs. * Females of childbearing potential must have a negative serum pregnancy test within 14 days of treatment. * Women of non-childbearing potential may be included if they are either surgically sterile or considered postmenopausal. Women who have documentation of at least 12 months of spontaneous amenorrhea and have an FSH level \>40mIU/mL will be considered postmenopausal. Exclusion Criteria: * Patients have a severe and/or uncontrolled medical disease (i.e., uncontrolled diabetes, chronic renal disease, or active uncontrolled infection). * Patients have known active brain metastasis. * Leptomeningeal disease * Patients have known chronic liver disease (i.e., cirrhosis) * Active or chronic infection with hepatitis C virus (HCV) or hepatitis B virus or known active or chronic infection with human immunodeficiency virus. Prior hepatitis infection that has been treated with highly effective therapy with no evidence of residual infection (including undetectable viral loads while on antiviral therapy) and with normal liver function (ALT, AST, total and direct bilirubin \</= ULN) is allowed * Known active tuberculosis * Concurrent active inoperable locally advanced or metastatic malignancy (other than malignancies, which the investigator determines are unlikely to interfere with treatment and safety analysis or are less of a treatment priority than their diagnosis of advanced GIST). * Patients have a history or current evidence of central serous retinopathy (CSR) or retinal vein occlusion (RVO) or predisposing factors to CSR or RVO (i.e. uncontrolled glaucoma or ocular hypertension, uncontrolled diabetes mellitus, hyperviscosity or hypercoagulability syndromes). * History of retinal degenerative disease. * History of Gilbert's syndrome. * Patients have clinically significant cardiovascular disease, including any of the following: 1) History of acute coronary syndrome including myocardial infarction, unstable angina, CABG, coronary angioplasty or stenting \< 6 months prior to screening; 2) symptomatic chronic heart failure (New York Heart Association Criteria, Class II-IV); 3) evidence of clinically significant cardiac arrhythmias and/or conduction abnormalities \< 6 months prior to screening except atrial fibrillation (AF) and paroxysmal supraventricular tachycardia (PSVT). * A screening Fridericia corrected QT interval (QTcF) ≥ 450 ms (men) or ≥ 470 ms (women). * Left ventricular ejection fraction (LVEF) \<50% as determined by a multigated acquisition (MUGA) scan or echocardiogram * Uncontrolled arterial hypertension defined as persistent elevation of systolic blood pressure ≥ 150 mmHg or diastolic blood pressure ≥ 100mmHg despite current therapy. * History of thromboembolic or cerebrovascular events ≤ 6 months prior to starting study treatment, including transient ischemic attacks, cerebrovascular accidents, deep vein thrombosis or pulmonary emboli * Patients who have neuromuscular disorders that are associated with elevated creatinine phosphokinase (i.e. inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis, spinal muscular atrophy). * Patients who are planning on embarking on a new strenuous exercise regimen after first dose of study treatment. NB: Muscular activities, such as strenuous exercise, that can result in significant increases in plasma CK levels should be avoided while on MEK162 treatment; * Impairment of gastrointestinal function or gastrointestinal disease (e.g., uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, ulcerative diseases, bowel resection with decreased intestinal absorption). * History of chronic inflammatory bowel disease or Crohn's disease requiring medical intervention (immunomodulatory or immunosuppressive medications or surgery) ≤ 12 months prior to randomization * Known history of acute or chronic pancreatitis * Patients had a major surgery within 3 weeks prior to study entry or who have not recovered from side effects of such procedure * Women who are pregnant or lactating. * Sexually active males unless they use a condom during intercourse while taking the drug and for 3 months after stopping treatment and should not father a child in this period. A condom is required to be used also by vasectomized men in order to prevent delivery of the drug via seminal fluid. * Patients with any significant history of non-compliance to medical regimens or with inability to grant reliable informed consent.