Patients will receive concurrent therapy with T-DM1 (3.6 mg/kg IV) on Day 1 of a 3-week (21 day) cycle and neratinib as a continuous daily oral dose. The neratinib dose-escalation will include 4 dose levels (120 mg, 160 mg, 200 mg, and 240 mg). At the recommended phase II dose (RP2D) of the T-DM1 and neratinib combination, up to 39 additional patients will be treated.