Inclusion criteria

• Measurable disease according to RECIST v1.1
• Eastern Cooperative Oncology Group (ECOG) Performance Status score of 0 or 1 Dose Escalation and Optimization Phase Inclusion Criteria
• Histologically or cytologically confirmed diagnosis of gastric or gastroesophageal junction adenocarcinoma or breast carcinoma
• Locally-advanced, unresectable, or metastatic stage
• Must have experienced disease progression on or after standard of care therapies or be intolerant of standard of care therapies. Cohort A (HER2-Low Breast Cancer) Inclusion Criteria
• Histologically or cytologically confirmed diagnosis of breast carcinoma
• Locally-advanced, unresectable, or metastatic stage
• HER2-low status determined by most recent local assessment (IHC 1+ or IHC 2+/ISH-negative)
• Prior therapies requirements
  • No more than 3 prior systemic cytotoxic chemotherapy regimens (including ADCs) for LA/mBC.
  • Participants with known BRCA mutation must have received a PARP-inhibitor where available and not medically contraindicated
  • Have progression on or after, or intolerant to, T-DXd, sacituzumab govitecan, or other topoisomerase I inhibitor therapies, if available as local standard of care therapy
  • Participants with HR+ tumors must have intolerance to endocrine therapy or endocrine therapy refractory disease:
• Prior therapies requirements
  • Participants with HR negative, HER2-low and PD-L1-positive (CPS 10 or greater) tumors must have received pembrolizumab with chemotherapy if available as local standard of care therapy.
  • Participants with HR negative, HER2-low and PD-L1-positive (CPS 10 or greater) tumors must have received pembrolizumab (or other PD-(L)1 inhibitor) with chemotherapy if available as local standard of care therapy and not medically contraindicated.
• Histologically or cytologically confirmed diagnosis breast carcinoma
• Locally-advanced, unresectable, or metastatic stage
• HER2+ status determined by most recent local assessment (IHC 3+ or IHC 2+/ISH+)
• Participants must have:
  • Received prior trastuzumab, pertuzumab and a taxane if available as local standard of care therapy for advanced disease.
  • Have progression on or after, or intolerant to, T-DXd or other topoisomerase I inhibitor therapies
  • No more than 3 prior systemic cytotoxic chemotherapy regimens (including ADCs) for LA/mBC
• Histologically or cytologically confirmed diagnosis of gastric or gastroesophageal junction adenocarcinoma
• Locally-advanced, unresectable, or metastatic stage
• HER2-low expression defined as IHC 1+ or IHC 2+/ISH-negative determined by most recent local assessment
• Willing and able to provide archival or newly obtained formalin-fixed paraffin-embedded (FFPE) tumor tissue blocks
• Participants must have received:
  • Prior systemic therapy with platinum, fluorouracil, or taxane for locally advanced unresectable or metastatic disease
  • Progression within 6 months of last dose of (neo)adjuvant cytotoxic chemotherapy is considered as 1 line of systemic therapy for LA/mGC/GEJC
  • Prior anti-PD-(L)1 therapy is allowed
  • No more than 2 prior systemic cytotoxic chemotherapy regimens (including ADC) for LA/mGC/GE
• Must not have received prior treatment with HER2 directed therapy Cohort D (HER2+ LA/mGC/GEJC) Inclusion Criteria
• Histologically or cytologically confirmed diagnosis of gastric or gastroesophageal junction adenocarcinoma
• Locally-advanced, unresectable, or metastatic stage
• HER2+ status determined by most recent local assessment (IHC 3+ or IHC 2+/ISH+)
• Participants must have:
  • Received prior trastuzumab plus fluoropyrimidine and platinum containing chemotherapy if no contraindication.
  • Prior T-DXd treatment is allowed
  • Prior PD1 inhibitor therapy is allowed
  • No more than 2 prior systemic cytotoxic chemotherapy regimens (including ADCs) for LA/mGC/GEJC
• Known hypersensitivity to any excipient contained in the drug formulation of disitamab vedotin or tucatinib
• Prior therapy with ADCs with MMAE payload
• Prior therapy with tucatinib
• Active CNS and/or leptomeningeal metastasis.
• Participants who have received prior systemic anticancer treatment including investigational agents within 4 weeks prior to first dose of study treatment
• History of other invasive malignancy within 3 years before the first dose of study intervention, or any evidence of residual disease from a previously diagnosed malignancy.
• Unable to swallow oral tablets or capsules or any significant GI disease which would preclude the adequate oral absorption of medications