This research study is designed to evaluate an experimental drug, MEDI4276, in treating breast and stomach (gastric) cancer.

Inclusion Criteria:

1. Age ≥ 18 years.

2. Histologically or cytologically documented unresectable, locally advanced or metastatic breast cancer or gastric cancer refractory to standard therapy.

   1. For subjects with breast cancer:

      • Prior treatment with trastuzumab, pertuzumab, and T-DM1, either alone or in combination, is required.
      • Subjects with a primary tumor that is hormone (estrogen, progesterone, or both) receptor-positive or receptor-negative are eligible.
      • Prior hormone therapy is allowed, but last dose must be at least 14 days prior to first dose of MEDI4276.

   2. For subjects with gastric cancer:

      • Prior treatment with a trastuzumab containing chemotherapy regimen is required.

3. HER2 Positive disease documented as FISH-positive and/or 3+ by IHC on previously collected tumor tissue.

4. At least one lesion measurable by RECIST Version 1.1.

Exclusion Criteria:

1. Receipt of any conventional or investigational anticancer treatment within 28 days prior to the first dose of MEDI4276.

2. History of exposure to the following cumulative doses of anthracyclines:

   1. Doxorubicin or liposomal doxorubicin >350 mg/m².
   2. Epirubicin >530 mg/m².
   3. Mitoxantrone >90 mg/m² and idarubicin > 70 mg/m².
   4. If another anthracycline or more than 1 anthracycline has been used, then the cumulative dose must not exceed the equivalent of 350 mg/m² of doxorubicin.

3. Known brain metastases that are untreated, symptomatic, or require therapy to control symptoms; or any radiation, surgery or other therapy to control symptoms from brain metastases within 2 months prior to first dose of MEDI4276.