This study will evaluate the safety, tolerability, and pharmacokinetics of Runimotamab administered intravenously as a single agent and in combination with Trastuzumab in participants with locally advanced or metastatic Human Epidermal Growth Factor Receptor 2 (HER2)-expressing cancers.

Inclusion Criteria

• Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1
• Life expectancy of at least 12 weeks
• Adequate hematologic and end-organ function
• Acute, clinically significant treatment-related toxicity from prior therapy must have resolved to Grade </=1 prior to study entry
• Left Ventricular Ejection Fraction (LVEF) >/=50%

HER2-Expressing Breast Cancer-Specific Inclusion Criteria

• Locally tested, Human Epidermal Growth Factor Receptor 2 (HER2)-expressing BC
• Locally advanced or metastatic BC that has relapsed or is refractory to established therapies

HER2-Expressing Gastric/Gastroesophageal (GEJ) Cancer-Specific Inclusion Criteria

• Adenocarcinoma of the stomach or GEJ with inoperable locally advanced or recurrent and/or metastatic disease, not amenable to curative therapy
• HER2-expressing tumor (primary tumor or metastasis) as assessed by local lab testing
• HER2-positive gastric/GEJ cancer must have received prior trastuzumab, cisplatin (or carboplatin or oxaliplatin or investigational platinum agent) and 5-fluorouracil (5-FU)/capecitabine

HER2-Positive Solid Tumor Specific Inclusion Criteria

• HER2-positive tumor (primary tumor or metastasis) as assessed by local (non-central) laboratory testing
• Locally advanced, recurrent, or metastatic incurable malignancy that has progressed after at least one available standard therapy; or for whom standard therapy has proven to be ineffective or intolerable, or is considered inappropriate; or for whom a clinical trial of an investigational agent is a recognized standard of care; or for whom a clinical trial of an investigational agent is considered an acceptable treatment option

Exclusion Criteria

• Pregnant or breastfeeding, or intending to become pregnant during the study or within 140 days after the last dose of runimotamab
• Significant cardiopulmonary dysfunction
• Known clinically significant liver disease
• Positive for acute or chronic Hepatitis B virus (HBV) infection
• Acute or chronic Hepatitis C virus (HCV) infection
• Human Immunodeficiency Virus (HIV) seropositivity
• Poorly controlled Type 2 diabetes mellitus
• History of ventricular dysrhythmias or risk factors for ventricular dysrhythmias
• Current treatment with medications that are well known to prolong the Q-wave/T-wave (QT) interval
• Known clinically significant liver disease
• Primary central nervous system (CNS) malignancy, untreated CNS metastases, or active CNS metastases (progressing or requiring corticosteroids for symptomatic control)
• Leptomeningeal disease
• Spinal cord compression that has not definitively treated with surgery and/or radiation
• History of autoimmune disease
• Prior allogeneic stem cell or solid organ transplantation