DESTINY-Gastric03 will investigate the safety, tolerability, pharmacokinetics, immunogenicity, and preliminary antitumor activity of trastuzumab deruxtecan (T-DXd) alone or in combination with chemotherapy and/or immunotherapy in HER2-expressing advanced/metastatic gastric/gastroesophageal junction (GEJ) and esophageal adenocarcinoma patients. Study hypotheses: Combination of T-DXd with cytotoxic chemotherapy and/or immunotherapy administered to subjects at the recommended phase 2 dose will show manageable safety and tolerability and preliminary anti-tumor efficacy so as to permit further clinical testing. T-DXd in combination with cytotoxic chemotherapy or immune checkpoint inhibitor administered to HER2-expressing gastric, GEJ and esophageal cancer patients who have not received prior treatment for advanced/metastatic disease will show preliminary evidence of anti-tumour activity and the potential to become a therapeutic option for this patient population.