• 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