Osimertinib, Cetuximab, and Tucatinib for the Treatment of EGFR-Mutant Stage IV or Recurrent Non-small Lung Cell Cancer

PRIMARY OBJECTIVE : I. To estimate the maximum tolerated dose (MTD) of osimertinib, cetuximab, and tucatinib in participants with EGFR-mutant non-small cell lung cancer (NSCLC) who have acquired resistance to EGFR-tyrosine kinase inhibitor (TKI). SECONDARY OBJECTIVES: I. To evaluate the toxicities of osimertinib, cetuximab, and tucatinib in participants with EGFR-mutant NSCLC who have acquired resistance to EGFR-TKI. II. To obtain preliminary assessment of anti-tumor activity of osimertinib, cetuximab, and tucatinib in participants with EGFR-mutant NSCLC who have acquired resistance to EGFR-TKI (osimertinib). III. To obtain preliminary assessment of anti-tumor activity of osimertinib, cetuximab, and tucatinib in the dose expansion cohort of participants with EGFR-mutant NSCLC who progressed on first-line osimertinib and do not have non-ERBB bypass tract mechanisms of resistance, including a subset of participants positive for HER2 aberrant signaling as determined by immunohistochemistry (IHC), fluorescence in situ hybridization (FISH) and/or next generation sequencing (NGS). OUTLINE: This is a dose-escalation study of tucatinib and cetuximab. Patients receive tucatinib 200mg orally BID, osimertinib 80mg orally daily, and cetuximab 250mg/m\^2 IV every 2 weeks of a 28-day cycle. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up at 30 days and every 12 weeks for up to 2 years.