A Combination Study of Kadcyla (Trastuzumab Emtansine) and Capecitabine in Participants With Human Epidermal Growth Factor Receptor 2 (HER2)-Positive Metastatic Breast Cancer (mBC) or HER2-Positive Locally Advanced/Metastatic Gastric Cancer (LA/mGC)

Inclusion Criteria:

Metastatic Breast Cancer

* Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2
* Adequate blood cell count
* Adequate liver, renal, and cardiac function
* Life expectancy greater than or equal to (\>/=) 12 weeks
* Histologically or cytologically confirmed breast cancer
* Confirmed HER2-positive disease, defined as immunohistochemistry (IHC) 3+ or in situ hybridization (ISH)-positive
* mBC with at least one measurable lesion according to RECIST v1.1
* Disease progression on at least one prior regimen containing trastuzumab and chemotherapy either separately or in combination; participants may be eligible to receive study therapy in first-line setting if trastuzumab and chemotherapy were given in the neoadjuvant/adjuvant setting
* Participant must have recovered from previous treatments

Locally Advanced/Metastatic Gastric Cancer

* ECOG performance status of 0, 1, or 2
* Adequate blood cell count
* Adequate liver, renal, and cardiac function
* Life expectancy \>/= 12 weeks
* Histologically or cytologically confirmed LA/mGC
* HER2-positive tumor (primary tumor or metastatic lesion), defined as either IHC 3+ or IHC 2+ and ISH-positive
* Inoperable LA/mGC

Exclusion Criteria:

Metastatic Breast Cancer

* Prior treatments before first study treatment:

  1. Investigational therapy within 28 days or 5 half-lives, whichever is longer
  2. Hormonal therapy within 14 days
  3. Trastuzumab within 21 days
* Prior treatment with trastuzumab emtansine or prior enrollment in a trastuzumab emtansine-containing study, regardless of whether the patient received trastuzumab emtansine
* Prior treatment with capecitabine
* History of severe or unexpected reactions to fluoropyrimidine or known hypersensitivity to fluorouracil
* Related capecitabine contraindications

  1. Treatment with sorivudine or chemically-related analogues
  2. Rare hereditary problems of galactose intolerance, Lapp lactase deficiency, or glucose-galactose malabsorption
  3. Complete absence of dihydropyrimidine dehydrogenase (DPD) activity
* History of intolerance or hypersensitivity to trastuzumab or murine proteins or any product component
* History of exposure to high cumulative doses of anthracyclines
* Brain metastases that are symptomatic or require radiation, surgery, or steroid therapy to control symptoms within 28 days before study drug
* Current peripheral neuropathy of Grade \>/=3
* History of other malignancy within the last 5 years, except for appropriately treated carcinoma in situ of the cervix, non-melanoma skin carcinoma, Stage I uterine cancer, or other cancers with a similar outcome
* Current unstable ventricular arrhythmia requiring treatment
* History of symptomatic congestive heart failure (CHF)
* History of myocardial infarction or unstable angina within 6 months prior to study drug
* History of left ventricular ejection fraction (LVEF) less than (\<) 40% or symptomatic CHF with previous trastuzumab treatment
* Severe dyspnea at rest due to complications of advanced malignancy or currently requiring continuous oxygen therapy
* Clinically significant malabsorption syndrome or inability to take oral medication
* Current severe, uncontrolled systemic disease (such as clinically significant cardiovascular, pulmonary, or metabolic disease)
* Major surgical procedure or significant traumatic injury within 28 days before enrollment or anticipation of the need for major surgery during study treatment
* Current known active infection with human immunodeficiency virus (HIV) or hepatitis B or C
* Lapatinib within 14 days before study drug

Locally Advanced/Metastatic Gastric Cancer

* Same as above, with addition of previous chemotherapy for advanced/metastatic disease (prior adjuvant/neoadjuvant therapy is allowed if at least 6 months has elapsed between completion of adjuvant/neoadjuvant therapy and enrollment into the study)