Inclusion Criteria:
* The patient must be able to provide written informed consent and follow the requirements specified in protocol.
* Age: ≥18 years.
* Life expectancy ≥6 months.
* Must have histologically or cytologically confirmed HER2-positive metastatic, unresectable cancer and must have had prior disease progression on all standard therapies for their tumor.
* Available archival tumor tissue (archival or from a new biopsy).
* At least one non-irradiated measurable tumor lesion according to RECIST v1.1.
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
* Acceptable liver, renal, hematologic and coagulation function.
Exclusion Criteria:
* Toxicities (except alopecia \& fatigue) due to prior antitumor therapy are higher than CTCAE v5.0 Grade 1.
* Toxicities due to radiotherapy (higher than grade 1) have not resolved to CTCAE v5.0 Grade ≤1 at least 21 days prior to the screening visit.
* Prior palliative or therapeutic radiation therapy to any RECIST v1.1 target lesion that defines baseline measurable disease for the study.
* Untreated or uncontrolled central nervous system (CNS) metastases.
* Any chemotherapy, biotherapy, immunotherapy, radiotherapy or other anti-tumor therapy within 3 weeks of the first dose of study treatment.
* Any severe cardiac dysfunction within 6 months of enrollment.
* Pulmonary embolism or deep vein thrombosis within 3 months prior to the first dose of study drug.
* Concurrent malignancy within 5 years prior to entry.
* Uncontrolled hypertension (systolic blood pressure \>160 mmHg or diastolic blood pressure \> 100 mmHg).
* History of ventricular tachycardia, or torsade des pointes.
* History of moderate to severe dyspnea at rest due to advanced malignancies or their complications, severe primary lung disease, current need of continuous oxygen therapy, or clinically active interstitial lung disease (ILD) or pneumonitis.
* Major surgery within 4 weeks of the first dose of study treatment and not fully recovered. Minor surgery within 2 weeks prior to study treatment.
* Known allergic reactions to any component or excipient of MRG002 or known allergic reactions to trastuzumab or other prior anti-HER2 or other monoclonal antibody ≥ Grade 3.
* Patients who have any known liver disease, including chronic hepatitis B, hepatitis C, autoimmune hepatic disorders, primary biliary cirrhosis or sclerosing cholangitis; Patients who have concurrent, serious, uncontrolled infections or known infection with HIV, or have a diagnosed acquired immunodeficiency syndrome (AIDS); or an uncontrolled autoimmune disease, or have undergone organ transplant.
* Active uncontrolled bacterial, viral, fungal, rickettsial, or parasitic infection.
* Any severe and/or uncontrolled systemic disease that at the discretion of investigator and sponsor makes it undesirable for the patient to participate in this study.
* Use of systemic corticosteroids within 4 weeks prior to the first dose of treatment.
* Use of strong CYP3A4 inhibitors.
* Pregnancy or breast-feeding.
