Phase 1 will use a 3+3 dose escalation design to evaluate escalating dose levels of tucatinib (ONT-380) in each of these three combinations in order to identify the maximal tolerated dose/recommended phase 2 dose (MTD/RP2D) of tucatinib (ONT-380). Capecitabine will be given at 1000 mg/m2 PO BID on Days 1-14 of each 21-day cycle. Trastuzumab will be given as a loading dose of 8 mg/kg IV followed by 6 mg/kg once every 21 days. However, a loading dose of trastuzumab will not be given to patients who have received trastuzumab within 4 weeks of the first study dose of trastuzumab. These patients will receive trastuzumab at 6 mg/kg each cycle, including Cycle 1. Trastuzumab may also be given on a weekly basis at 2 mg/kg IV q 7 days, but only in the circumstance that trastuzumab infusion has been delayed, and weekly infusions are required to resynchronize the cycle length to 21 days, after discussion with the medical monitor. Trastuzumab infusion rates will be per institutional guidelines. Tucatinib (ONT-380) will be given PO BID at a dose dependent upon the dosing cohorts to which the patient is enrolled.