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

Key Inclusion Criteria: * Participant must be willing and capable of giving written Informed Consent, adhering to dosing and visit schedules, and meeting all study requirements * Participant has histologically or cytologically confirmed locally advanced or metastatic non-small cell lung cancer (NSCLC) that is not amenable to treatment with curative intent * Prior treatment status: * Cohorts 1 and 2: Participant has had at least one prior systemic treatment for locally advanced or metastatic NSCLC * Cohorts 3 and 4: Participant is treatment-naïve for locally advanced or metastatic NSCLC and eligible to receive first-line treatment with poziotinib as determined by the Investigator. Adjuvant/neo-adjuvant therapies (chemotherapy, radiotherapy, or investigational agents) are permissible as long as they end at least 15 days prior to study entry. * Cohort 5: Participants who meet the criteria for enrollment in Cohorts 1 to 4, but the enrollment in the respective cohort has been closed * Cohort 6: Participant with EGFR mutation-positive NSCLC who progressed while on treatment with first-line osimertinib * Cohort 7: Participant has had at least one prior systemic treatment for locally advanced or metastatic NSCLC * Specific mutations: * Cohort 1 and 3: Documented EGFR exon 20 insertion mutation * Cohort 2 and 4: Documented HER2 exon 20 insertion mutation * Cohort 5: Documented EGFR or HER2 exon 20 insertion mutations * Cohort 6: Documented acquired EGFR mutation (tested after osimertinib progression) * Cohort 7: Documented EGFR or HER2 activating mutations * Participant has adequate organ function at Baseline Key Exclusion Criteria: * Participant 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. The currently approved TKIs (ie, erlotinib, gefitinib, afatinib, osimertinib) are not considered to be exon 20 insertion-selective and are permissible (Cohorts 1 and 2). * Participant is concurrently receiving chemotherapy, biologics, immunotherapy for cancer treatment; systemic anti-cancer treatment or investigational treatment should not be used within 2 weeks or 5 half lives, whichever is longer; local radiation therapy for bone pain may be allowed * Participant 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 * Participant is pregnant or breast-feeding