DS8201a and Pembrolizumab in Participants With Locally Advanced/Metastatic Breast or Non-Small Cell Lung Cancer

Inclusion Criteria: * Written informed consent * Adults ≥18 years * Eastern Cooperative Oncology Group performance status (ECOG PS) 0 to 1 * Pathologically documented HER2-expressing locally advanced/metastatic breast cancer, and HER2-expressing or HER2-mutant locally advanced/metastatic NSCLC * Willing to provide a tumor biopsy during screening and during treatment * Have at least 1 measurable lesion per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 as assessed by the Investigator * Adequate cardiac function, as defined by left ventricular ejection fraction (LVEF) ≥50% within 28 days before enrollment. * Adequate organ function * Adequate treatment washout period before enrollment Inclusion Criteria Specific to Part 1 * Participants in Part 1 should meet the additional inclusion criteria listed for 1 of the 4 cohorts in Part 2. Inclusion Criteria Specific to Part 2 Inclusion Criteria for Cohort 1 * Pathologically documented, locally advanced/metastatic breast cancer that has centrally determined HER2-positive expression as per American Society of Clinical Oncology-College of American Pathologists (ASCO-CAP) Guidelines * Received prior trastuzumab emtansine (T-DM1) therapy with documented progression Inclusion Criteria for Cohort 2 * Pathologically documented, locally advanced/metastatic breast cancer that has centrally determined HER2-low expression (immunohistochemistry \[IHC\] 1+ or IHC 2+/in situ hybridization \[ISH-\]) * Participants must have exhausted treatments that can confer any clinically meaningful benefit (eg, other therapies such as hormonal therapy for participants who are hormone receptor positive) Inclusion Criteria for Cohort 3 * Pathologically documented, locally advanced/metastatic NSCLC that has centrally or locally determined HER2-expression (IHC 1+, 2+, or 3+) * Participants who have known epidermal growth factor receptor (EGFR) mutation, anaplastic lymphoma kinase (ALK), BRAF V600E mutation, or ROS1 fusion should have disease progression after treatment with at least one genomically-targeted therapy for metastatic disease that are known to confer clinical benefit, or are intolerant to treatment, or refuse standard treatment Inclusion Criteria for Cohort 4 * Pathologically documented, locally advanced/metastatic HER2-mutant NSCLC * Participants who have known EGFR mutation, ALK, BRAF V600E mutation, or ROS1 fusion should have disease progression after treatment with at least one genomically-targeted therapy for metastatic disease that are known to confer clinical benefit, or are intolerant to treatment, or refuse standard treatment Exclusion Criteria: * Prior treatment with pembrolizumab or DS-8201a * Medical history of myocardial infarction (MI) within 6 months before enrollment, symptomatic congestive heart failure (New York Heart Association Class II to IV). Participants with troponin levels above the upper limit of normal at Screening (as defined by the manufacturer), and without any MI-related symptoms, should have a cardiologic consultation before enrollment to rule out MI * Corrected QT interval (QTc) prolongation to \>470 ms (females) or \>450 ms (males) * History of (non-infectious) interstitial lung disease (ILD)/pneumonitis that required steroids, has current ILD/pneumonitis, or where suspected ILD/pneumonitis cannot be ruled out by imaging at screening * Spinal cord compression or clinically active central nervous system metastases * Active, known or suspected autoimmune disease * Condition requiring systemic treatment with either corticosteroids (\>10 mg daily prednisone equivalent) or other immunosuppressive medications within 14 days of start of study treatment * Prior therapy with an anti-PD-1 or anti-PD-L1 agent * Prior therapy with an agent directed to another stimulatory or coinhibitory T-cell receptor (eg, CTLA-4, OX 40, CD137) and was discontinued from that treatment due to a Grade 3 or higher immune-related adverse event (irAE) * Prior anti-HER2 therapy is not allowed for participants with HER2 low-expressing breast cancer or participants with NSCLC (Cohorts 2, 3, or 4). Prior treatment with pan-HER tyrosine kinase inhibitor is allowed. * Prior systemic anticancer therapy, including investigational agents within 2 to 6 weeks prior to treatment * Unresolved toxicities from previous anticancer therapy * Live vaccine within 30 days prior to the first dose of study drug * Currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study treatment * Multiple primary malignancies within 3 years, except adequately resected non-melanoma skin cancer, curatively treated in situ disease, other solid tumors curatively treated, or contralateral breast cancer * History of severe hypersensitivity reactions to other monoclonal antibodies and/or any of the study drug components * Active infection requiring systemic therapy * Known history of human immunodeficiency virus (HIV) infection * Active hepatitis B or C virus infection * History or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the participant's participation for the full duration of the study, or is not in the best interest of the participant to participate, or any other reason the participant is found not appropriate to participate in the opinion of the treating Investigator * Known psychiatric or substance abuse disorders * Prior organ transplantation, including allogeneic stem cell transplantation * Pregnant, breastfeeding, or planning to become pregnant * Clinically severe pulmonary compromise resulting from intercurrent pulmonary illnesses * Uncontrolled infection requiring IV antibiotics, anti-virals, or anti-fungals