Basket Study of Tucatinib and Trastuzumab in Solid Tumors With HER2 Alterations

Inclusion Criteria * Histologically or cytologically confirmed diagnosis of locally-advanced unresectable or metastatic solid tumor, including primary brain tumors * Participants with non-squamous NSCLC must have progressed during or after standard treatment or for which no standard treatment is available * Participants with other disease types must have progressed during or after ≥1 prior line of systemic therapy for locally-advanced unresectable or metastatic disease * Disease progression during or after, or intolerance of, the most recent line of systemic therapy * Disease demonstrating HER2 alterations (overexpression/amplification or HER2 activating mutations), as determined by local or central testing processed in a Clinical Laboratory Improvement Amendments (CLIA)- or International Organization for Standardization (ISO) accredited laboratory, according to one of the following: * HER2 overexpression/amplification from fresh or archival tumor tissue or blood * Known activating HER2 mutations detected in fresh or archival tumor tissue or blood * Have measurable disease per RECIST v1.1 criteria according to investigator assessment * Have Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 Exclusion Criteria * Participants with breast cancer, gastric or gastroesophageal junction adenocarcinoma, or CRC whose disease shows HER2 amplification/overexpression. * Previous treatment with HER2-directed therapy; participants with uterine serous carcinoma or HER2-mutated gastric or gastroesophageal junction adenocarcinoma without HER2-overexpression/amplification may have received prior trastuzumab * Known hypersensitivity to any component of the drug formulation of tucatinib or trastuzumab (drug substance, excipients, murine proteins), or any component of the drug formulation of fulvestrant in participants with HR+ HER2-mutated breast cancer * History of exposure to a 360 mg/m² doxorubicin-equivalent or \>720 mg/m\^2 epirubicin-equivalent cumulative dose of anthracyclines * Treatment with any systemic anti-cancer therapy, radiation therapy, major surgery, or experimental agent within ≤3 weeks of first dose of study treatment or are currently participating in another interventional clinical trial. There are additional inclusion and exclusion criteria. The study center will determine if criteria for participation are met.