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.