Phase 2 Study of Poziotinib in Participants With NSCLC Having EGFR or HER2 Exon 20 Insertion Mutation

The Screening period (Day -30 to Day -1) lasts up to approximately 30 days prior to Cycle 1, Day 1. Participant must meet all Inclusion/Exclusion Criteria to participate in the study. Eligible participants will provide written Informed Consent prior to undergoing any study procedures. Each treatment cycle is 28 calendar days in duration. There will be seven participant cohorts and eligible participants will be enrolled into each cohort in parallel based on epidermal growth factor receptor (EGFR) or human epidermal growth factor receptor 2 (HER2) exon 20 mutation status and prior treatment status: * Cohort 1: Previously treated participant with EGFR exon 20 insertion mutation positive NSCLC (complete) * Cohort 2: Previously treated participant with HER2 exon 20 insertion mutation positive NSCLC (complete) * Cohort 3: Treatment naïve participant with EGFR exon 20 insertion mutation positive NSCLC (complete) * Cohort 4: Treatment naïve participant with HER2 exon 20 insertion mutation positive NSCLC (fully enrolled) * Cohort 5: Participants who meet the criteria for enrollment in Cohort 1 to 4, but the enrollment in the respective cohort has been closed (closed to enrollment) * Cohort 6: Participants with acquired EGFR mutation who progressed while on treatment with first-line osimertinib (closed to enrollment) * Cohort 7: Participants with EGFR or HER2 activating mutations (closed to enrollment) Toxicity will be assessed based on the grade of the adverse events using CTCAE version 4.03. On Day 1 of each 28-day cycle, the participant's absolute neutrophil count (ANC) must be ≥1.5×10\^9/L and platelet count must be ≥100×10\^9/L before administering poziotinib. All participants will be treated until disease progression (except for first progression in Cohort 5), death, intolerable adverse events (AEs), or other protocol-specified reasons for participant withdrawal.