TAS2940 is a small molecule inhibitor of ERBB family proteins HER2 and EGFR. It has not been evaluated in human subjects yet. The study will be conducted in 2 parts, dose escalation and dose expansion. The dose escalation part will assess the safety and determine the maximum tolerated dose, the recommended phase 2 dose and the recommended dosing regimen of TAS2940 administered orally. The dose expansion part will assess preliminary anti-tumor activity in select solid tumors characterized by HER2 or EGFR aberrations.