Primary Objectives:~● To determine the intracranial antitumor activity of the tucatinib and ado-trastuzumab emtansine (T-DM1) combination per the modified Response Evaluation Criteria in Solid Tumors (mRECIST) in patients with human epidermal growth factor receptor 2 (HER2)-positive metastatic solid tumors and brain metastases.~Key Secondary Objectives:~To determine the intracranial antitumor activity of the tucatinib and T-DM1 combination per the Response Assessment in Neuro-Oncology Brain Metastases (RANO-BM) criteria in patients with HER2-positive metastatic solid tumors and brain metastases.~To evaluate the duration of intracranial response of the tucatinib and T-DM1 combination in patients with HER2-positive metastatic solid tumors and brain metastases.~Other Secondary Objectives:~To evaluate the safety and tolerability of the tucatinib and T-DM1 combination in patients with HER2-positive metastatic solid tumors and brain metastases.~To evaluate the systemic antitumor activity of the tucatinib and T-DM1 combination per the Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 in patients with HER2-positive metastatic solid tumors and brain metastases.~To evaluate progression-free survival (PFS) in patients with HER2-positive metastatic solid tumors and brain metastases receiving the tucatinib and T-DM1 combination.~To evaluate overall survival (OS) in patients with HER2-positive metastatic solid tumors and brain metastases receiving the tucatinib and T-DM1 combination.~To evaluate the duration of response to the tucatinib and T-DM1 combination per the RECIST v1.1 in patients with HER2-positive metastatic solid tumors and brain metastases.~To evaluate the clinical benefit rate of the tucatinib and T-DM1 combination per the RECIST v1.1 in patients with HER2-positive metastatic solid tumors and brain metastases.~Exploratory Objectives:~To evaluate the pharmacokinetics (PK) of the tucatinib and T-DM1 combination.~To assess the effects of the tucatinib and T-DM1 combination on cell proliferation and apoptosis.~To evaluate predictive and pharmacodynamic (PD) biomarkers of response and resistance to the tucatinib and T-DM1 combination.~To assess the effects of the tucatinib and T-DM1 combination on circulating-free DNA (cfDNA) dynamics.
To learn if the study drugs, tucatinib and adotrastuzumab emtansine (T-DM1), can help to control solid tumors that have spread to the brain.