Key Inclusion Criteria:

          -  Patient must be willing and capable of giving written Informed Consent, adhering to
             dosing and visit schedules, and meeting all study requirements

          -  Previously treated patient with histologically or cytologically confirmed (archival
             tissue accepted) locally advanced or metastatic non-small cell lung cancer (NSCLC) and
             is not a candidate for definitive therapy

               -  Phase 1: No test for mutational status is required

               -  Phase 2: Documented EGFR or HER2 exon 20 insertion mutations (including
                  duplication mutations) in NSCLC patients

          -  Prior treatment status:

               -  Phase 1: Patient with refractory NSCLC to available standard therapies

               -  Phase 2: Progression after at least one systemic therapy for locally advanced or
                  metastatic disease

          -  Patient has measurable NSCLC disease, as per the Response Evaluation Criteria in Solid
             Tumors (RECIST, version 1.1). Metastatic lesions in bone, CNS, or in brain cannot be
             used for target lesions.

          -  Patient has recovered from prior systemic therapy for metastatic disease to Grade ≤1
             for non-hematologic toxicities (except for Grade ≤2 peripheral neuropathy) and has
             adequate hematologic, hepatic, and renal function at Baseline

        Key Exclusion Criteria:

          -  Patient is concurrently receiving chemotherapy, biologics, immunotherapy for cancer
             treatment; systemic anti-cancer treatment or investigational treatment should not be
             used within 2 weeks prior to Cycle 1, Day 1; local radiation therapy for bone pain may
             be allowed

          -  Patient has used strong inhibitors/inducers of CYP3A4 and CYP2D6 within 1 month prior
             to Cycle 1, Day 1

          -  Patient has had another primary malignancy within 3 years prior to starting study
             treatment, except for adequately treated basal or squamous cell carcinoma of the skin
             or cancer of the cervix in situ

          -  Patient is pregnant or breastfeeding

          -  Phase 2 : Patient has had previous treatment with poziotinib. The currently approved
             TKIs that are not considered to be exon 20 insertion-selective are permissible