This is an open, multicenter phase Ib/II clinical study. The goal of this study is to confirm the Phase II recommended dose (RP2D) of AK129 combinations for advanced solid tumors and evaluate the safety and efficacy of AK129 combinations for non-small cell lung cancer (NSCLC), head and neck squamous cell carcinoma (HNSCC), colorectal adenocarcinoma (CRC), and other advanced solid tumors.

Inclusion Criteria:

1. Be able and willing to provide written informed consent and to comply with all requirements of study participation (including all study procedures);
2. ≥18 years old and ≤ 75 years (regardless of sex);
3. ECOG performance status 0-1;
4. Life expectancy longer than 3 months;
5. 1)Histologically or cytologically confirmed diagnosis of Stage IIIB/C or IV NSCLC (American Joint Committee on Cancer [AJCC]); 2)No prior systemic anti-tumor therapy for locally advanced or metastatic NSCLC;must have received a platinum-based combination therapy and a PD-(L)1 monoclonal antibody for the treatment of locally advanced or metastatic disease and progressed during or after receiving prior therapy;
6. 1)Histologically or cytologically confirmed diagnosis of recurrent or metastatic HNSCC (American Joint Committee on Cancer [AJCC]); 2)No prior systemic anti-tumor therapy for recurrent or metastatic HNSCC ;must have received a platinum-based combination therapy and a PD-(L)1 monoclonal antibody for the treatment of recurrent or metastatic disease and progressed during or after receiving prior therapy;
7. Histologically or cytologically confirmed diagnosis of advanced colorectal adenocarcinoma with microsatellite stabilization;
8. Measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1;
9. Adequate organ function.

Exclusion Criteria:

1. Histologically or cytologically confirmed the presence of small cell carcinoma components/EGFR-sensitive mutations or ALK fusion positivite/known ROS1 rearrangement, MET exon 14 skipping mutation, EGFR exon 20 insertion mutation, BRAF V600E mutation, NTRK gene fusion positivite or RET gene fusion positivite;
2. Histologically or cytologically confirmed diagnosis of advanced colorectal adenocarcinoma with microsatellite highly unstable/mismatch repair gene expression defect (MSI-H/dMMR)or histopathological examination confirmed other pathological types;
3. Participating in another clinical research;
4. Has known active central nervous system (CNS) metastases, brain stem/meningeal metastasis, spinal cord metastasis or compression;
5. Has an active autoimmune disease that has required systemic treatment in the past 2 years;
6. Has known active tuberculosis (TB) and suspected active TB should be ruled out by clinical examination; known active syphilis infection; known active Hepatitis B or Hepatitis C;
7. Past or currently has non-infectious pneumonia/interstitial lung disease that requires systemic glucocorticoid therapy;
8. Has pleural effusion, pericardial effusion, or ascites that have clinical symptoms or require repeated drainage;
9. Had a history of myocarditis, cardiomyopathy, and malignant arrhythmia;
10. Has known allergy to any component of any investigational drug; a known history of severe hypersensitivity to other monoclonal antibodies;
11. Pregnant or lactating female.