This main purpose of this clinical study is to learn about the safety and activity of margetuximab and pembrolizumab combination treatment in patients with HER2+ gastric and gastroesophageal junction cancer.

Detailed Description: Both margetuximab and pembrolizumab are monoclonal antibodies used in combination to treat HER2+ gastric and gastroesophageal junction cancer. This study has two parts: Dose Escalation and Dose Expansion. The Dose Escalation phase of the study will evaluate safety of escalating doses of the combination treatment. The Dose Expansion phase will evaluate safety and activity of the combination in patients with gastric or gastroesophageal cancer once the final dose and schedule are defined. In addition, a cohort of patients with HER2+ 3+ gastric cancer patients will be enrolled in the Dose Expansion Phase.

Inclusion Criteria:

1. Signed written informed consent.
2. Age ≥ 18 years old (or minimum age based upon local regulations)
3. Unresectable locally advanced or metastatic histologically proven HER2+ gastroesophageal junction (GEJ) or gastric cancer. Gastric Cancer Expansion Phase will include only gastric cancer patients with 3+ HER2 positivity.
4. HER2+ as 3+ (as defined in AJCC staging manual 8th edition) by IHC or in-situ hybridation (ISH) amplified.
5. Have received prior treatment with trastuzumab.
6. Have received treatment with at least one or more lines of cytotoxic chemotherapy in the metastatic setting.
7. Resolution of chemotherapy, immunotherapy or radiation-related toxicities.
8. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
9. Life expectancy ≥ 12 weeks.
10. Measurable disease as per RECIST 1.1 criteria.

Exclusion Criteria:

1. Patients with symptomatic central nervous system (CNS) metastases.
2. Patients with any history of known or suspected autoimmune disease with the specific exceptions of vitiligo, atopic dermatitis, or psoriasis not requiring systemic treatment.
3. History of prior allogeneic bone marrow, stem-cell or solid organ transplantation.
4. Treatment with any systemic anti-neoplastic therapy, or investigational therapy within the 3 weeks prior to the initiation of study drug.
5. Treatment with radiation therapy within 3 weeks prior to the initiation of study drug administration.
6. Treatment with corticosteroids (≥10 mg per day prednisone or equivalent) or other immune suppressive drugs within the 14 days prior to the initiation of study drug administration.
7. History of clinically-significant cardiovascular disease.
8. Clinically-significant pulmonary compromise, including a requirement for supplemental oxygen use to maintain adequate oxygenation.
9. History of (non-infectious) pneumonitis that required steroids or presence of active pneumonitis
10. Clinically-significant gastrointestinal disorders, such as perforation, gastrointestinal bleeding, or diverticulitis.
11. Evidence of active viral, bacterial, or systemic fungal infection.