This clinical trial is designed to evaluate the safety, pharmacokinetics, pharmacodynamics, and preliminary efficacy of MT-304 in adults with advanced HER2-expressing solid tumors. The main questions it aims to answer are:

• What is the safety profile of MT-304 when administered alone or with nivolumab?
• What is the recommended Phase 2 dose (RP2D) of MT-304?

Participants will:

• Receive MT-304 alone (every 14 days) or with nivolumab (every 28 days).
• Attend regular clinic visits for assessments and monitoring.
• Continue treatment until disease progression, unacceptable toxicity, or study discontinuation.

This multicenter, open-label, Phase 1 trial is designed to assess the safety, tolerability, pharmacokinetics (PK), pharmacodynamics (PD), and preliminary efficacy of MT-304 in adults aged 18 and older with advanced HER2-expressing solid tumors.

The study consists of two treatment modules:

• Module 1 (Monotherapy): Participants receive MT-304 every 14 days for 28-day cycles, with dosing adjustments based on clinical benefit and safety evaluations.
• Module 2 (Combination Therapy): Participants receive MT-304 in combination with nivolumab, administered every 14 days and 28 days, respectively, also allowing for dosing adjustments.

The Bayesian Optimal Interval (BOIN) design will guide dose escalation, overseen by a Safety Review Committee to establish the recommended Phase 2 dose (RP2D).

Regular assessments, including vital signs and laboratory tests, will monitor safety and efficacy throughout the trial, with follow-up visits for up to 2 years post-treatment.

Inclusion Criteria:

• Aged 18 years or above
• Histologically confirmed diagnosis of metastatic or advanced epithelial cancer expressing HER2 (Note: Participants with other tumor types expressing HER2 may be considered pending discussion with the Medical Monitor).
• Measurable lesion per RECIST 1.1 criteria.
• Eastern Cooperative Oncology Group (ECOG) performance status Grade of 0 or 1.
• Adequate Organ function

Exclusion Criteria:

• Known active CNS metastasis and/or carcinomatous meningitis.
• Any acute illness including fever.
• History of symptomatic congestive heart failure
• History of (noninfectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease.
• Uncontrolled pleural effusion, pericardial effusion, or ascites
• Active autoimmune disease not related to prior therapy for primary malignancy that has required systemic therapy in the last 1 year.