Inclusion Criteria:

          1. Age 18 years old or older.

          2. Able to swallow and retain orally administered medication and does not have any
             clinically significant gastrointestinal abnormalities that may alter absorption such
             as malabsorption syndrome or major resection of the stomach or bowels.

          3. Women of childbearing potential must have a negative serum pregnancy test within 3
             days prior to Cycle 1 Day 1 and agree to use effective contraception, throughout the
             treatment period, and for 4 months after the last dose of study treatment.

             .

          4. Patients must have histologically or cytological confirmed stage IIIB or IV non-small
             cell lung cancer.

          5. Documented ALK-rearrangement (or ROS1 rearrangement for phase I only) break-apart
             fluorescence in situ hybridization (FISH) (in at least 15% of tumor cells), or next
             generation sequencing assay performed on tumor sample or cell-free DNA in Clinical
             Laboratory Improvement Amendments (CLIA)-approved laboratory.

          6. Measurable disease defined by RECIST 1.1 criteria

          7. Eastern Cooperative Oncology Group (ECOG) Performance status of 0-2.

          8. Life expectancy of at least 3 months.

          9. Resolution of all acute toxic effects of prior chemotherapy, immunotherapy,
             radiotherapy or surgical procedures to ≤ grade 2 (CTCAE v 4.0). Exception to this
             criterion: patients with any grade of alopecia are allowed to enter the treatment.

         10. The following laboratory criteria have been met:

               -  Absolute neutrophil count (ANC) ≥ 1.5 x 109/L

               -  Hemoglobin (Hgb) ≥ 9 g/dL

               -  Platelets ≥ 75 x 109/L

               -  Prothrombin time (PT) / international normalized ratio (INR) and Partial
                  thromboplastin time (PTT) ≤1.5 x upper limit of normal (ULN)

               -  Serum creatinine ≤ 1.5 mg/dL and /or calculated creatinine clearance (using
                  Cockcroft-Gault formula) ≥ 30 mL/min

               -  Albumin 2.5 g/dL

               -  Total bilirubin ≤ 1.5 x ULN, except for patients with Gilbert's syndrome who may
                  be included if total bilirubin ≤ 3.0 x ULN or direct bilirubin ≤ 1.5 x ULN

               -  Aspartate transaminase (AST) ≤ 2.5 x ULN; alanine transaminase (ALT) ≤ 2.5 x ULN,
                  except for patients with liver metastasis, who are only included if AST and ALT <
                  5 x ULN

               -  Alkaline phosphatase (ALP) ≤ 5.0 x ULN

               -  Fasting plasma glucose ≤ 175 mg/dL (≤ 9.8 mmol/L)

               -  Serum amylase ≤ 2 x ULN

               -  Serum lipase ≤ ULN

         11. Patient must have the following laboratory values or have the following laboratory
             values corrected with supplements to be within normal limits before the first dose of
             ceritinib + trametinib:

               -  Potassium

               -  Magnesium

               -  Phosphorus

               -  Total calcium (corrected for serum albumin)

         12. Left Ventricular Ejection fraction (LVEF) ≥ lower limit of normal (LLN) by
             echocardiogram (ECHO) or multigated acquisition scan (MUGA)

         13. Patient has the ability to understand and provide signed informed consent.

         14. Willingness and ability to comply with scheduled visits, treatment plans, laboratory
             tests and other study procedure.

         15. Specific inclusion criteria for the phase II dose expansion cohorts:

        Documented ALK-rearranged stage IIIB or IV NSCLC and:

          -  Cohort A: No prior ALK inhibitor therapy (prior chemotherapy or immunotherapy is
             allowed).

          -  Cohort B: Prior treatment with crizotinib and documented disease progression by RECIST
             1.1 criteria.

          -  Cohort C: Prior treatment with 2nd generation ALKi (e.g. ceritinib, alectinib,
             loratinib, or brigatinib) and documented disease progression by RECIST 1.1 criteria.

        Exclusion Criteria:

          1. Patients with known hypersensitivity to any of the excipients of ceritinib
             (microcrystalline cellulose, mannitol, crospovidone, colloidal silicon dioxide and
             magnesium stearate).

          2. Patient has history of interstitial lung disease or interstitial pneumonitis,
             including clinically significant radiation pneumonitis (i.e., affecting activities of
             daily living or requiring therapeutic intervention).

          3. Patient who has received thoracic radiotherapy to lung fields ≤4 weeks prior to
             starting the study treatment or patients who have not recovered from
             radiotherapy-related toxicities. For all other anatomic sites (including radiotherapy
             to thoracic vertebrae and ribs) radiotherapy ≤2 weeks prior to starting the study
             treatment or has not recovered from radiotherapy-related toxicities. Palliative
             radiotherapy for bone lesions ≤2 weeks prior to starting study treatment is allowed.

          4. Prior systemic anti-cancer treatment (chemotherapy, immunotherapy, biologic therapy,
             vaccine therapy, or investigational treatment) within the last 3 weeks, or
             chemotherapy without delayed toxicity within the last 2 weeks preceding the first dose
             of the combination. Prior systemic treatment in the adjuvant setting is allowed.

          5. Patient has clinically significant, uncontrolled heart disease and/or recent cardiac
             event (within 6 months), such as:

               -  unstable angina within 6 months prior to screening;

               -  myocardial infarction within 6 months prior to screening;

               -  history of documented congestive heart failure (New York Heart Association
                  functional classification III-IV);

               -  Uncontrolled hypertension defined by a Systolic Blood Pressure (SBP) ≥ 160 mm Hg
                  and/or Diastolic Blood Pressure (DBP) ≥ 100 mm Hg, with or without
                  antihypertensive medication

               -  initiation or adjustment of antihypertensive medication(s) is allowed prior to
                  screening;

               -  ventricular arrhythmias

               -  supraventricular and nodal arrhythmias not controlled with medication;

               -  other cardiac arrhythmia not controlled with medication;

               -  corrected QT (QTcF) > 470 ms using Fridericia's correction on the screening
                  electrocardiogram (ECG)

          6. Patient has impairment of gastrointestinal (GI) function or GI disease that may
             significantly alter the absorption of orally administered medication (e.g., ulcerative
             diseases, uncontrolled nausea, vomiting, diarrhea, or malabsorption syndrome).

          7. Receiving medications that meet one of the following criteria and that cannot be
             discontinued at least 1 week prior to the start of treatment with ceritinib and for
             the duration of participation:

               -  Medication with a known risk of prolonging the QT interval or inducing Torsades
                  de Pointes (please refer to
                  http://www.azcert.org/medical-pros/drug-lists/drug-lists.cfm)

               -  Strong inhibitors or strong inducers of CYP3A4/5 (please refer to
                  http://medicine.iupui.edu/flockhart/table.htm or
                  http://www.druginteractioninfo.org)

               -  Medications with a low therapeutic index that are primarily metabolized by
                  CYP3A4/5, and/or CYP2C9 (please refer to
                  http://medicine.iupui.edu/flockhart/table.htm or
                  http://www.druginteractioninfo.org)

               -  Therapeutic doses of warfarin sodium (Coumadin) or any other coumadin-derived
                  anti-coagulant. Anticoagulants not derived from warfarin are allowed (eg,
                  dabigatran, rivaroxaban, apixaban).

               -  Unstable or increasing doses of corticosteroids; If patients are on
                  corticosteroids for endocrine deficiencies or tumor-associated symptoms, dose
                  must have been stabilized (or decreasing) for at least 5 days before first dose
                  of study treatment.

               -  Enzyme-inducing anticonvulsive agents

               -  Herbal supplements

          8. Pregnant or nursing (lactating) women, where pregnancy is defined as the state of a
             female after conception and until the termination of gestation, confirmed by a
             positive human Chorionic Gonadotropin (hCG) laboratory test.

          9. Women of child-bearing potential, defined as all women physiologically capable of
             becoming pregnant, unless they are using highly effective methods of contraception
             during dosing and for 3 months after the last dose of study treatment. Highly
             effective contraception methods include:

               -  Total abstinence (when this is in line with the preferred and usual lifestyle of
                  the subject. Periodic abstinence (e.g., calendar, ovulation, symptothermal,
                  post-ovulation methods) and withdrawal are not acceptable methods of
                  contraception.

               -  Female sterilization (have had surgical bilateral oophorectomy with or without
                  hysterectomy) or tubal ligation at least six weeks before taking study treatment.
                  In case of oophorectomy alone, only when the reproductive status of the woman has
                  been confirmed by follow up hormone level assessment.

               -  Male sterilization (at least 6 months prior to screening) with the appropriate
                  post-vasectomy documentation of the absence of sperm in the ejaculate. For female
                  subjects on the study the vasectomized male partner should be the sole partner
                  for that subject.

               -  Combination of any two of the following (a+b or a+c or b+c):

                    1. Use of oral, injected or implanted hormonal methods of contraception or
                       other forms of hormonal contraception that have comparable efficacy (failure
                       rate < 1%), for example hormone vaginal ring or transdermal hormone
                       contraception.

                    2. Placement of an intrauterine device (IUD) or intrauterine system (IUS).

                    3. Barrier methods of contraception: Condom or Occlusive cap (diaphragm or
                       cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal
                       suppository.

             In case of use of oral contraception, women should have been stable on the same pill
             for a minimum of 3 months before taking study treatment.

             Women are considered post-menopausal and not of child bearing potential if they have
             had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical
             profile. (e.g., age appropriate, history of vasomotor symptoms) or have had surgical
             bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six
             weeks prior to screening. In the case of oophorectomy alone, only when the
             reproductive status of the woman has been confirmed by follow up hormone level
             assessment is she considered not of child bearing potential.

         10. Sexually active males unless they use a condom during intercourse while taking drug
             and for 3 months after the last dose of study treatment. Male patients for 3 months
             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.

         11. Patient has a history of pancreatitis or history of increased amylase or lipase that
             was due to pancreatic disease.

         12. Patient has 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.

         13. Patient has had major surgery (e.g., intra-thoracic, intra-abdominal or intra-pelvic)
             within 4 weeks prior to starting study treatment or has not recovered from side
             effects of such procedure. Video-assisted thoracic surgery (VATS) and mediastinoscopy
             will not be counted as major surgery and patients can receive study treatment ≥ 1 week
             after these procedures.

         14. History of another malignancy. Exception: Subjects who have been disease-free for 3
             years, or subjects with a history of completely resected non-melanoma skin cancer
             and/or subjects with indolent (early stage breast cancer or prostate cancer) second
             malignancies are eligible after discussion with the study principle investigator (PI).

         15. History of retinal vein occlusion (RVO)

         16. Symptomatic brain metastases or leptomeningeal (LM) disease requiring corticosteroids
             for symptom management. Asymptomatic brain metastases or LM will be allowed on study.

         17. Known Human Immunodeficiency Virus (HIV), Hepatitis B Virus (HBV), or Hepatitis C
             Virus (HCV) infection (subjects with laboratory evidence of cleared HBV and HCV
             infection will be permitted).