This multicenter study will assess the maximum tolerated dose of capecitabine in combination with Kadcyla (trastuzumab emtansine) in participants with HER2-positive mBC or HER2-positive LA/mGC using a Phase I design, followed by a randomized, open-label Phase II study to explore the efficacy and safety of the combination of Kadcyla and capecitabine compared with Kadcyla alone in mBC. The anticipated time on study treatment is until disease progression, intolerable toxicity, or withdrawal of consent.