This is a Phase 2, open-label, multicenter study to evaluate the efficacy and the
      safety/tolerability of poziotinib in two patient cohorts for up to 114 previously treated
      NSCLC patients with any systemic therapy (57 patients with EGFR exon 20 insertion mutations
      and 57 patients with HER2 exon 20 insertion mutations).
    
      The Screening period (Day -30 to Day -1) lasts up to approximately 30 days prior to Cycle 1,
      Day 1. Patients must meet all Inclusion/Exclusion Criteria to participate in the study.
      Eligible patients will provide written Informed Consent prior to any study procedures.
      Each treatment cycle is 28 calendar days in duration. There will be two patient cohorts and
      eligible patients will be enrolled into each cohort in parallel based on EGFR or HER2 exon 20
      mutation status:
        -  Cohort 1 : Previously treated patients with EGFR exon 20 insertion mutation positive
           NSCLC (N=57)
        -  Cohort 2 : Previously treated patients with HER2 exon 20 insertion mutation positive
           NSCLC (N=57) Toxicity will be assessed based on the severity grade of the adverse events
           using CTCAE version 4.03.
      Poziotinib (16 mg) will be taken orally, once daily (QD) with food and a glass of water at
      approximately the same time each morning.
      All patients will be treated until disease progression, death, intolerable adverse events
      (AEs), or other protocol-specified reasons for patient withdrawal.
    
        Inclusion Criteria:
          1. Patient is at least 18 years of age (or country's legal age of majority if the legal
             age was > 18 years) at the time of obtaining informed consent.
          2. Patient must be willing and capable of giving written Informed Consent, adhering to
             dosing and visit schedules, and meeting all study requirements
          3. Patient has histologically confirmed locally advanced or metastatic non-small cell
             lung cancer (NSCLC) that is not amenable to treatment with curative intent
          4. Patient has had at least one prior systemic treatment for NSCLC, but no more than
             three prior systemic therapy
          5. Patient has adequate tumor tissue obtained from a biopsy or surgical procedure to
             enable molecular profiling for central laboratory confirmation of the mutation.
          6. Patient is positive for EGFR or HER2 exon 20 mutations based on tissue testing:
               -  Cohort 1: Documented EGFR exon 20 insertion mutation (including duplication
                  mutations)
               -  Cohort 2: Documented HER2 exon 20 insertion mutation (including duplication
                  mutations)
          7. Patient has measurable disease, as per the Response Evaluation Criteria in Solid
             Tumors (RECIST, version 1.1). Metastatic lesions in CNS or in brain cannot be used for
             target lesions.
          8. Brain metastases may be allowed if patient's condition is stable.
          9. Patient has an Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 and
             has a life-expectancy of more than 6 months
         10. 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
         11. Patient is willing to practice 2 forms of contraception, one of which must be a
             barrier method, from study entry until at least 30 days after the last dose of
             poziotinib
         12. Females of childbearing potential must have a negative pregnancy test within 30 days
             prior to enrollment. Females who are postmenopausal for at least 1 year (defined as
             more than 12 months since last menses) or who are surgically sterilized do not require
             this test.
        Exclusion Criteria:
          1. Patient has EGFR T790M mutation or any other acquired EGFR exon 20 point mutation
          2. Patient has had previous treatment with poziotinib or any other EGFR or HER2 exon 20
             insertion mutation-selective tyrosine kinase inhibitor (TKI) prior to study
             participation.
          3. Patient has had radiotherapy (intention for cure) or surgery (other than surgical
             placement for vascular access and minimally invasive procedures including some biopsy
             procedures) within 2 weeks prior to start of study treatment with poziotinib
          4. Patient has a history of congestive heart failure (CHF) Class III/IV according to the
             New York Heart Association (NYHA) Functional Classification or serious cardiac
             arrhythmias requiring treatment
          5. Patient has a high risk of cardiac disease, as determined by the Investigator, may
             undergo either echocardiogram (ECHO) or multi-gated acquisition (MUGA) during
             Screening and has a cardiac ejection fraction <50%.
          6. Patient has had other malignancies within the past 3 years, except for stable
             non-melanoma skin cancer, fully treated and stable early stage prostate cancer or
             carcinoma in situ of the cervix or breast without need of treatment
          7. Patient is confirmed to have clinically significant or recent acute gastrointestinal
             disease presenting as diarrhea and/or coloenteritis as a main symptom.
          8. Patient has an active Grade ≥2 skin disorder, rash, mucositis, or skin infection that
             needs medication or therapy or existing Grade ≥2 skin toxicity from previous
             therapies.
          9. Presence or history of interstitial lung disease (ILD), drug-induced ILD, or presence
             of radiation pneumonitis
         10. Patient is unable to take drugs orally due to disorders or diseases that may affect
             gastrointestinal function, such as inflammatory bowel diseases or malabsorption
             syndrome, or procedures that may affect gastrointestinal function
         11. Patient has an active liver disease or biliary tract disease (except for Gilbert's
             disease, asymptomatic biliary stones, liver metastasis, or stabilized chronic liver
             diseases)
         12. Patient has known hypersensitivity to poziotinib or has a history of allergic
             reactions attributed to chemically similar compounds or other tyrosine kinase
             inhibitors (TKIs)
         13. Patient has an active uncontrolled infection, underlying medical condition, or other
             serious illness that would not be appropriate for this study
         14. Patient has unstable, uncontrolled, active bleeding disorders that the investigator
             considers that the patient could be at increased risk or not be suitable for treatment
             in this study
         15. Patient is pregnant or breast-feeding.