Inclusion Criteria:

        Key Inclusion Criteria:

          -  Subjects with histologically or cytologically confirmed metastatic or locally advanced
             unresectable gastric adenocarcinoma or gastroesophageal junction (GEJ) adenocarcinoma
             positive for MUC17. Subjects should not be eligible for curative surgery and should
             have been refractory to or have relapsed after two or more prior lines of standard
             systemic therapy that included a platinum, a fluoropyrimidine, either a taxane or
             irinotecan, and an approved vascular endothelial growth factor receptor (VEGFR)
             antibody/tyrosine kinase inhibitor (TKI).

          -  For subjects eligible for human epidermal growth factor receptor 2 (HER2) directed
             therapy, prior systemic therapy should have included a HER2 targeting antibody
             approved for treatment of gastric cancer.

          -  Subjects may also be included if the aforementioned therapeutic options were medically
             not appropriate for them. In these cases, the reason(s) why required prior therapies
             for gastric cancer were medically not appropriate should be documented in the
             subject's electronic case report form (eCRF).

          -  For dose expansion only: Subjects with at least one measurable lesion ≥ 10mm which has
             not undergone biopsy within 3 months of screening scan. This lesion cannot be biopsied
             at any time during the study.

        Exclusion Criteria:

        Key Exclusion Criteria:

          -  Any anticancer therapy or immunotherapy within 4 weeks of start of first dose.

          -  Central nervous system (CNS) metastases, leptomeningeal, or spinal cord compression.

          -  Autoimmune disorders requiring chronic systemic steroid therapy or any other form of
             immunosuppressive therapy. Subjects may be included if the treatment is discontinued
             more than 3 months prior to the first dose of AMG 199, there is a low likelihood of
             relapse from the autoimmune disorder, AND there is agreement between the investigator
             and the Amgen Medical Monitor.