Patients receive TORC1/2 inhibitor INK128 orally (PO) once daily (QD) on days 1, 3, 5, 8, 10, 12, 15, 17, 19, 22, 24, and 26 (day 1 is omitted in course 1). Patients also receive EGFR inhibitor AZD9291 PO QD on days 1-28. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.