Inclusion Criteria:  Aged ≥ 18, regardless of gender. Subjects with histologically or cytologically confirmed diagnosis of metastatic or unresectable advanced NSCLC or other solid tumors (including but not limited to head and neck cancer, colorectal, etc.) who have disease progression on, or were not resistant to, or reject the standard treatment. For Part 1, subjects must be diagnosed with EGFR positive and/or MET positive after testing. For Part 2, patients need to undergo the centralized biomarker testing. Subjects of the dose escalation phase in Part 1 must have evaluable diseases, and others must have measurable diseases as defined in RECIST v1.1. Eastern Cooperative Oncology Group (ECOG) performance status scores are 0-1. Expected survival is ≥3 months.  With certain organ system functions (without transfusion, use of blood components, or G-CSF support within 14 days before testing), as defined below:  Absolute Neutrophil Count (ANC) ≥1.5×10^9 /L Platelet count (PLT）≥75×10^9 /L Hemoglobin (HB) ≥10 g/dL Total bilirubin ≤1.5 times the upper limit of normal (ULN) Alanine amino transferase (ALT) and aspartate amino transferase (AST) ≤3×ULN Creatinine ≤1.5×ULN. If creatinine is >1.5×ULN, creatinine clearance is ≥50 mL/min as calculated by Cockcroft-Gault formula, or ≥50 mL/min within 24 h as measured, the patients can still be included. Willing to and capable of following the trial and follow-up schedule. Capable of understanding the trial nature and voluntarily signing the written informed consent form. The subjects of Part 2 must agree that the tumor tissue samples before treatment of the investigational drug can be collected or provided.  Exclusion Criteria:  Use of certain investigational drug or antineoplastic agent within 14 days before first administration of MCLA-129 or within 5 half lives (whichever is longer). Execution of large surgery and radiotherapy (except focal palliative radiotherapy at least 2 weeks before first administration), immunotherapy, chemotherapy (for Nitrosoureas or Mitomycin C and other chemotherapeutics with delayed toxicity, it shall be 6 weeks before first administration) within 4 weeks before first administration of MCLA-129. Patients with colorectal who are diagnosed with AS or BRAF gene mutation through testing. Subjects with NSCLC who previously received more than 2 lines of cytotoxicity chemotherapy for treatment of focal advanced or metastatic disease (excluding maintenance therapy). Subjects who previously received EGFR-TKI (e.g. Poziotinib or TAK-788) that is known to be effective to exon 20 insertion mutation Prior use of EGFR/c-Met bispecific antibody drugs. Response of toxic reactions related to prior therapy (except alopecia) not up to Grade 1 or below (CTCAE 5.0 criteria) before first administration of MCLA-129. With other malignant tumors in the past 3 years, except cancers that have been cured significantly or can be focally cured, e.g. basosquamous carcinoma of skin, carcinoma cervix in situ, or in situ breast carcinoma. Patients with primary malignant tumor of central nervous system, or metastases to meninges, or concomitantly with symptomatic brain metastases, or new therapy naive brain metastases.  With clinically significant cardiovascular disorder, including but not limited to:  Deep vein thrombosis or lung embolism diagnosed within 1 month before first administration of the investigational drug. Non-obstructive catheter related clot and other clinically irrelevant thrombosis are not included in the exclusion criteria. With any of the following medical history within 6 months before first administration of the investigational drug: myocardial infarction, unstable angina, stroke, transient ischemic attack, coronary or peripheral artery bypass, or any acute coronary syndrome. With abnormal ECG corrected QT interval (QTcF) at rest in the screening period. Re-measurement is made twice at an interval of 4 h above. For average QTcF of 3 ECG inspections: male: ≥ 450 msec, and female: ≥ 470 msec. With clinically significant abnormal heart rate, conduction, and ECG form at rest, e.g. complete left bundle branch block, third-degree conduction block, second-degree conduction block, and PR interval > 250 msec. Poorly controlled hypertension in the investigator's opinion (systolic blood pressure > 180 mmHg, or diastolic blood pressure > 100 mmHg). New York Heart Association Grade III-IV congestive heart failure, or hospitalization due to congestive heart failure within 6 months before first administration of the investigational drug. Pericarditis/clinically significant pericardial effusion. Cardiomyopathy. With clinically significant cardiovascular disorder as believed by other investigators. Active hepatitis B (hepatitis B surface antigen (HBsAg) or hepatitis B core antibody (HBcAb) positive, and serum HBV DNA ≥ 2000 IU/mL (equal to 104 copies/mL)), hepatitis C virus antibody, HIV antibody and treponema pallidum antibody positive. Patients with Interstitial lung disease, including drug-induced Interstitial lung disease or radiation pneumonitis. Current severe disease or medical condition, including but not limited to uncontrolled active infection, and clinically significant lung, metabolic or psychiatric disorders. Women with child bearing potential, pregnant women or lactating women with pregnancy test positive 7 days before treatment, and male and female unwilling to take effective contraception measures or having a birth plan during the treatment and within 3 months after end of treatment. Patients who are known to have allergic reactions and hypersensitivity reactions, or be allergic to MCLA-129 or any other excipients. Patients poorly compliant, unable or unwilling to follow the study and/or follow-up procedure listed in the protocol, or patients unsuitable to participate in this trial in the investigator's opinion.