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.