Study of Trametinib + Ceritinib in Patients With Unresectable Melanoma

Inclusion Criteria: * Diagnosis of advanced/unresectable melanoma (AJCC v.8 Stage 3C/D/4) * Measurable disease, defined as per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Must have at least one tumor site accessible for a biopsy * Documented disease refractory to at least one PD1/PD-L1 (+/- CTLA-4) inhibitor treatment, or intolerance to these drugs and if BRAFV600-mutant melanoma, refractory disease to at least one BRAF and MEK inhibitor (defined as progression while on treatment), or intolerance to these drugs * Last line of treatment prior to study enrollment must not have been BRAF/MEK inhibitor therapy * Prior treatment-related toxicity resolved to ≤ Grade 2 or baseline * Prior radiation allowed * Eastern Cooperative Oncology Group (ECOG) performance status ≤2 * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation and for 90 days after completion of trametinib + ceritinib administration. * Participants must have normal organ and marrow function. Exclusion Criteria: * Potential participants with known hypersensitivity to any of the excipients of trametinib, ceritinib (microcrystalline cellulose, mannitol, crospovidone, colloidal silicon dioxide and magnesium stearate). * An untreated or uncontrolled brain metastases or evidence of leptomeningeal disease. Patients with asymptomatic brain metastases or previously treated brain metastases that are stable (i.e., not requiring corticosteroids) at the time of study start will be eligible. * Previous malignancy is not an exclusion provided that the other malignancy is considered under control, patient is not on concomitant anti-cancer drug therapy, and target lesions from melanoma are clearly defined for response assessment. * Other severe, acute, or chronic medical conditions including uncontrolled diabetes mellitus or psychiatric conditions or laboratory abnormalities that, in the opinion of the investigator, may increase the risk associated with study participation or may interfere with the interpretation of study results. * Clinically significant, uncontrolled heart disease and/or recent cardiac event (within 6 months), such as: 1. unstable angina within 6 months prior to screening; 2. myocardial infarction within 6 months prior to screening; 3. history of documented congestive heart failure (New York Heart Association functional classification III-IV); 4. cardiac arrhythmias not controlled with medication; 5. Corrected QT (QTcF) \>470 ms at baseline * A history of interstitial lung disease or interstitial pneumonitis, including clinically significant radiation pneumonitis (i.e., affecting activities of daily living or requiring therapeutic intervention). (Note, this does NOT include immune-mediated pneumonitis) * Impaired gastrointestinal (GI) function or GI disease that may alter absorption of study drugs or inability to swallow * Receiving medications that meet one of the following criteria and that cannot be discontinued at least 1 week prior to start of treatment with study drugs and for the duration of participation: 1. Medication with a known risk of prolonging the QT interval or inducing Torsades de Pointes 2. Strong inhibitors or strong inducers of CYP3A4/5, and Medications with a low therapeutic index that are primarily metabolized by CYP3A4/5, and/or CYP2C9 3. Therapeutic doses of warfarin sodium (Coumadin) or any other coumadin-derived anti-coagulant. Anticoagulants not derived from warfarin are allowed (e.g., dabigatran, rivaroxaban, apixaban). 4. Unstable or increasing doses of corticosteroids in the 5 days before first dose of study treatment. 5. Enzyme-inducing anticonvulsive agents