A Study of Tucatinib (MK-7119) in Combination With Trastuzumab and Capecitabine in Participants With Previously Treated Locally Advanced Unresectable or Metastatic Human Epidermal Growth Factor Receptor 2 Positive (HER2+) Breast Carcinoma (MK-7119-001)

Inclusion Criteria: * Has histologically confirmed HER2+ breast carcinoma * Has received previous treatment with taxane anti-cancer agent, trastuzumab, pertuzumab, and T-DM1 with the exception of when the use of taxanes is contraindicated or judged not to be the best treatment at the investigator's discretion * Has radiographically and/or histologically confirmed disease progression on last systemic anticancer treatment * Has adequate organ function * Female participant is not pregnant or breastfeeding and is not a woman of childbearing potential (WOCBP) or is a WOCBP and using contraception or abstinent from heterosexual intercourse during the intervention period and for at least 30 days after receiving the last dose of tucatinib, 80 days after receiving the last dose of trastuzumab, or 180 days after receiving the last dose of capecitabine, whichever occurs last and agrees to not donate eggs during this period * Male participants refrain from donating sperm and are either abstinent from heterosexual intercourse or agree to use contraception during the intervention period and for at least 7 days after receiving the last dose of tucatinib and 90 days after receiving the last dose of capecitabine, whichever occurs last * Previously treated brain metastasis is stable or progressed, provided there is no clinical indication for immediate re-treatment Exclusion Criteria: * Has been previously treated with lapatinib within 12 months of starting study treatment * Has been previously treated with neratinib, afatinib, tucatinib or capecitabine * Has a history of exposure to doxorubicin, epirubicin, mitoxantrone, idarubicin, liposomal doxorubicin * Has had treatment with any systemic anti-cancer therapy including hormonal therapy, non-central nervous system (CNS) radiation or experimental agent ≤3 weeks before first dose of study treatment * Has any toxicity related to prior cancer therapies that has not resolved with the exception of alopecia, congestive heart failure, anemia * Has clinically significant cardiopulmonary disease * Has known myocardial infarction or unstable angina within 6 months prior to the first dose of study treatment * Has any uncontrolled viral, bacterial or fungal infection within 14 days prior to the first dose of study treatment * Is positive for Hepatitis B, Hepatitis C or has known chronic liver disease * Is known to be positive for human immunodeficiency virus (HIV) * Has evidence within 2 years of the start of study treatment of another malignancy that required systemic treatment * Has ongoing use of systemic corticosteroids for control of symptoms of brain metastases * Has any brain lesion thought to require immediate local therapy * Has known or suspected leptomeningeal disease (LMD) * Has poorly controlled generalized or complex partial seizures or manifest neurologic progression due to brain metastases