Inclusion Criteria:

          -  Ability to understand and provide informed consent.

          -  Willingness and ability to comply with scheduled study visits and procedures.

          -  Adult men or women age ≥ 18 years.

          -  Histologic or cytologic diagnosis of advanced/metastatic Non-small Cell Lung Cancer
             (NSCLC), stage IIIB/IV.

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.

          -  1 - 3 (no more than three) prior regimens for stage IIIB/IV disease, with at least one
             prior regimen (for any stage) containing a platinum-based agent. One prior PD-1 or
             PD-L1 antibody-based regimen is allowable and counts as a prior regimen. Prior therapy
             with a taxane is allowed.

          -  Participants enrolled on the phase 1b expansion portion of the trial must be willing
             and able 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 3 months prior to
             initiation of treatment on Day 1, and must be obtained after most recent tumor
             progression. Participants for whom newly-obtained samples cannot be provided (e.g.,
             inaccessible or participant safety concern) may submit an archived specimen only upon
             agreement from the Sponsor.

          -  Prior radiation is allowed if patients have recovered from side effects.

          -  Potential participants with a prior history of brain metastases are eligible,
             provided:

               -  The brain metastases have been treated

               -  The patient is asymptomatic from the brain metastases

               -  Corticosteroids prescribed for the management of brain metastases have been
                  discontinued at least 7 days before registration to study

               -  The brain metastases are stable on pre-registration imaging

               -  There is no evidence of leptomeningeal disease

          -  Measurable metastatic disease according to Response Evaluation Criteria in Solid
             Tumors (RECIST) v1.1.

          -  Life expectancy > 3 months.

          -  Must have adequate organ and marrow function.

          -  Must have adequate laboratory values.

          -  Participants of child bearing potential must not be pregnant and must use established
             contraceptive strategies as outlined in the study protocol.

        Exclusion Criteria:

          -  Rearrangements in ALK.

          -  Activating mutations in EGFR.

          -  Potential participants with active malignancies other than NSCLC, or prior curatively
             treated malignancy at high risk of relapse during the study period with the exception
             of localized squamous or basal cell skin cancers.

          -  Pregnant or breast feeding.

          -  Known hypersensitivity to ceritinib, docetaxel, or any of their excipients.

          -  Serious uncontrolled medical disorder, psychiatric condition 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.

          -  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 are exceptions
             and patients can receive study treatment ≥1 week after these procedures.

          -  A history of clinically significant noninfectious interstitial pneumonitis (i.e.,
             limiting activities of daily living or requiring therapeutic intervention), including
             clinically significant radiation pneumonitis.

          -  Residual toxicity from prior anticancer therapy of grade 3 or greater (CTCAE v5.0),
             with the exception of alopecia

          -  Concurrent use of other anticancer approved or investigational agents within 2 weeks
             of the first dose of study treatment.

          -  In taxane pretreated patents, any history of dose-limiting toxicity with prior taxane
             therapy.

          -  A clinically significant, uncontrolled heart disease and/or recent cardiac event
             (within 6 months).

          -  Uncontrolled diabetes mellitus, defined as fasting plasma glucose > 200 mg/dL.

          -  Impaired gastrointestinal (GI) function or GI disease that may alter absorption of
             ceritinib, or inability to swallow capsules

          -  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 QT interval or inducing Torsades de
                  Pointes

               -  Strong inhibitors or strong inducers of CYP3A4/5 (see Appendix A for list)

               -  Medications with a low therapeutic index that are primarily metabolized by
                  CYP3A4/5, and/or CYP2C9

               -  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)

               -  Enzyme-inducing anticonvulsive agents

               -  Herbal medications, including but not limited to: St. John's wort, Kava, ephedra
                  (ma huang), gingko biloba, dehydroepiandrosterone (DHEA), yohimbe, saw palmetto,
                  and ginseng.