This study is being done to see if tucatinib with ado-trastuzumab emtansine (T-DM1) works better than T-DM1 alone to help patients who have a specific type of breast cancer called HER2 positive breast carcinoma. The breast cancer in this study is either metastatic (spread into other parts of the body) or cannot be removed completely with surgery. Patients in this study will be randomly assigned to get either tucatinib or placebo (a pill with no medicine). This is a blinded study, so neither patients nor their doctors will know whether a patient gets tucatinib or placebo. All patients in the study will get T-DM1, a drug that is often used to treat this cancer. Each treatment cycle lasts 21 days. Patients will swallow tucatinib pills or placebo pills two times every day. Patients will get T-DM1 injections from the study site staff on the first day of every cycle.