Main inclusion criteria :  Males or females aged ≥ 18 years at the time of signing the informed consent form. For Part 1 of this study, the subjects should be ≤ 75 years of age. Patients for Part 1: patients histopathologically diagnosed with advanced or recurrent solid tumors or more line SOC failure or progression within 6m after adjuvant or neoadjuvant therapy.  For Part 2 of the study, patients with histopathologically confirmed advanced hepatocellular carcinoma; Barcelona Clinic Liver Cancer (BCLC) stage C or B; where stage B patients must be unsuitable for surgical and/or local therapy, or have progressive disease after surgical and/or local therapy, or refuse surgical and local therapy.  Cohort 1: Patients with advanced HCC who have not received previous treatment with anti-PD-1 pathway drugs (including anti-PD-1, anti-PD-L1 or anti-PD-L2 drugs), including patients who have received or have not received systemic treatment (e.g. anti-VEGF/VEGFR monoclonal antibodies, anti-VEGFR-TKIs, chemotherapy); patients who have received adjuvant/neoadjuvant therapy with anti-PD-1 pathway drugs and have disease progression more than 12 months after the end of treatment can be enrolled into this cohort Cohort 2: advanced HCC patients who have progressed during or after anti-PD-1 pathway drug therapy (with clearly documented radiographic evidence of progression), including patients who have or have not received systemic therapy (e.g., anti-VEGF/VEGFR monoclonal antibodies, anti-VEGFR-TKIs, chemotherapy); patients who have progressed within 6 months after the end of adjuvant/neoadjuvant therapy with anti-PD-1 pathway drugs may be enrolled into this cohort Other possible tumor expansion cohorts will be further revised as more data become available. Patients must be able to provide fresh tumor tissues or archived tumor tissues. Patients whose estimated survival time is more than 3 months. Patients with at least one measurable lesion at baseline according to RECIST (Version 1.1). Patients with Eastern Cooperative Oncology Group (ECOG) performance status score ≤ 1. Patients whose organ function must meet the study requirements: Every woman or man with potential fertility needs to use an effective contraceptive method. Willing and able to comply with study-specified visits schedule, treatment plan, laboratory examination and other study procedures.  Main exclusion criteria:  Patients who are simultaneously participating in another clinical study, unless the study is an observational (non-interventional) clinical study or the patient is already in the survival follow-up period of the interventional study. Patients with a history of severe allergic diseases, a history of severe drug allergies, and known or suspected allergy to macromolecular protein preparations or HBM4003 excipients or toripalimab excipients. For the liver cancer cohort in Part 2 of the study, patients with pathological findings suggestive of fibrolamellar hepatocellular carcinoma, sarcomatoid hepatocellular carcinoma, cholangiocarcinoma, or mixed hepatocellular carcinoma-cholangiocarcinoma were excluded. Previous and concomitant drugs or treatments to be excluded like CTLA4, PD-1,PD-L1. Insufficient recovery from previous treatments Diseases that may affect the efficacy and safety of the investigational product. A history of other malignant diseases within 5 years before the first dose. Symptomatic, active, or urgent treatment-requiring central nervous system (CNS) metastasis with imaging evidence (based on CT or MRI assessment). Subjects with pleural effusion, pericardial effusion, or ascites Patients with severe liver cirrhosis, liver atrophy or hypertension. Imaging revealed that the main portal vein tumor thrombus was more than 1/2, and the vein tumor thrombus or heart was involved. Grade ≥ 2 hepatic encephalopathy within 12 months, or currently requiring medication to prevent or control hepatic encephalopathy. Patients who the investigator believes may have other factors that will affect the efficacy or safety evaluation of this study (e.g., mental disorders, alcoholism, drug use, etc.). Women who are pregnant or breastfeeding, or who plan to become pregnant during the study period and within 3 months after the last administration of the investigational product.