The primary purpose of this study is to characterize the safety and tolerability of tucatinib (MK-7119) in Chinese participants with human epidermal growth factor receptor 2 positive (HER2+) advanced breast cancer, gastric or gastroesophageal junction adenocarcinoma (GEC), and colorectal cancer.

Inclusion Criteria:

• Histologically or cytologically confirmed HER2+ advanced breast cancer, gastric or GEC, and colorectal cancer
• Have progressed at least one previous therapeutic regimen and either no longer are candidates for standard therapy, have no standard therapy available, or choose not to pursue standard therapy
• Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Performance within 7 days prior to allocation
• Has life expectancy >6 months in the opinion of the investigator
• Have measurable disease per Response Evaluation Criteria in Solid Tumours (RECIST) 1.1 as assessed by the local site investigator/radiologist
• Must test negative for hepatitis B surface antigen (HBsAg)
• If there is a history of hepatitis C virus (HCV) infection, has undetectable HCV viral load at screening
• For males, agree to be abstinent from heterosexual intercourse, or agree to use acceptable contraception, for the duration of study and 1 week after
• For females, is not pregnant or breastfeeding AND one of the following applies:
• Is not a woman of childbearing potential (WOCBP)
• Is a WOCBP and uses highly effective contraception and is not pregnant

Exclusion Criteria:

• History of prior cancer within <3 year, except for adequately treated basal cell or squamous cell carcinoma of the skin, cervical cancer in situ, or other in situ carcinomas which needs discussion between the investigator and the Sponsor
• Participants with leptomeningeal disease are excluded
• Has symptomatic central nervous system (CNS) metastases
• Has active human immunodeficiency virus (HIV), hepatitis B virus, or HCV infection
• Has had chemotherapy, immunotherapy, radioimmunotherapy, definitive radiation, or biological cancer therapy or treatment with an investigational product within 4 weeks (2 weeks for palliative radiation) before the first dose of study intervention
• Has an active infection requiring therapy
• Has refractory nausea/vomiting, chronic gastrointestinal disease, or significant bowel resection
• Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study
• Has a QTc prolongation
• Has uncontrolled illness including but not limited to ongoing symptomatic congestive heart failure (New York Heart Association [NYHA] Class III or IV heart failure), unstable angina pectoris, cardiac arrhythmia, and psychiatric illness that would limit compliance with study requirements
• Has had major surgery within 4 weeks prior to first dose of study intervention
• Is currently participating in another clinical trial
• Has psychiatric or substance abuse disorder