Ligufalimab and Cadonilimab in Advanced Liver Cancers

Inclusion Criteria: 1. Histological confirmation of specific disease -Cohort A (HCC): Patient must have a diagnosis confirmed by histology or clinically by the American Association for the Study of Liver Diseases (AASLD) criteria in patients with cirrhosis. Known fibrolamellar HCC will be excluded. * Cohort B (BTC, biliary tract cancers): Patients must have histologically confirmed biliary tract cancer (including intrahepatic cholangiocarcinoma, extrahepatic cholangiocarcinoma, and gall bladder cancers). Patients with combined HCC-cholangiocarcinoma may be enrolled in Cohort B. 2. Locally advanced or metastatic disease * Patients with locally advanced or metastatic disease must have disease deemed not amenable to surgical and/or locoregional therapies or patients who have progressed following surgical and/or locoregional therapies. * Measurable disease, as defined as lesions that can accurately be measured in at least one dimension according to RECIST version 1.1 at least 1 cm with contrast enhanced dynamic imaging (magnetic resonance imaging or computed tomography). 3. Refractory to or relapsed after prior anti-PD-1/L1 antibody therapy. May have received anti-PD-1/L1 monotherapy or combination therapy as any line of therapy including in the neoadjuvant or adjuvant setting. Patients who discontinued prior immune checkpoint inhibitor treatment due to a high-grade toxicity (Grade 4) are not eligible. 4. For patients in cohort A who do not have a clinical diagnosis of HCC according to the AASLD criteria, formalin-fixed, paraffin-embedded (FFPE) tumor diagnostic tissue samples must have been obtained within 4 years from the time of consent. Baseline tissue will be requested any time after consent. It is strongly recommended that tissue is obtained from standard-of-care biopsies confirming progression of disease on prior therapy so that the patient has not received any intervening systemic anti-cancer treatment from the time that the baseline tissue was obtained. 5. Prior locoregional therapy is allowed provided the following are met: 1) at least 2 weeks since prior locoregional therapy including surgical resection, chemoembolization, radiotherapy, or ablation; 2) target lesion has increased in size ≥25% since the cessation of locoregional therapy or the target lesion was not treated with locoregional therapy. Patients treated with palliative radiotherapy for symptoms will be eligible as long as the target lesion is not the treated lesion and radiotherapy will be completed at least 2 weeks prior to study drug administration. 6. Age ≥ 18 years 7. Child-Pugh Score A or B7 (only applicable for Cohort A) 8. ECOG Performance score of 0-1 9. Adequate organ and marrow function (without chronic, ongoing growth factor support or transfusion in the last 2 weeks) as defined below: -Platelet count ≥ 50,000/mm3 -Hgb ≥ 9 g/dl -Absolute neutrophil ≥ 1,000 cells/mm3 -Total bilirubin ≤ 3 mg/ml (This will not apply to subjects with Gilbert's syndrome who have persistent or recurrent hyperbilirubinemia that is predominantly unconjugated in the absence of hemolysis, or patients with hyperbilirubinemia secondary to distal malignant obstruction where endoscopic, surgical, or percutaneous bypass/stenting has been attempted. Such patients may be enrolled based in consultation with the principal investigator) -INR ≤ 2 -AST, ALT ≤ 5 times ULN * Calculated creatinine clearance (CrCl) ≥ 40 mL/min. CrCl can be calculated using the Cockroft-Gault method. * Albumin ≥ 2.0 g/dl 10. All men, as well as women of child-bearing potential, defined as not surgically sterilized and between menarche and 1-year post menopause, must agree to use highly effective contraception methods (hormonal or barrier method of birth control or abstinence) 4 weeks prior to study entry, for the duration of study participation, and for 120 days after the last dose of ligufalimab or cadonilimab. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. A female of child-bearing potential is any woman (regardless of sexual orientation, marital status, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria: * Has not undergone a hysterectomy or bilateral oophorectomy; or * Has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months). 11\. Women of child-bearing potential must have a negative serum pregnancy test at screening. 12\. Subjects are eligible to enroll if they have non-viral-HCC, or if they have HBV-HCC, or HCV-HCC defined as follows: 1\) HBV-HCC: Hepatitis B subjects will be allowed if they meet the following criteria: On antiviral therapy for HBV. Subjects who are anti-HBc (+), negative for HBsAg, negative for anti-HBs, and have an HBV viral load under 100 IU/mL do not require HBV anti-viral prophylaxis. 2\) HCV-HCC: Active or resolved HCV infection as evidenced by detectable HCV RNA or antibody. Patients who have failed HCV therapy as evidenced by detectable HCV RNA will be eligible. Subjects with chronic infection by HCV who are treated (successfully or treatment failure) or untreated are allowed on study. 13\. Ability to understand and the willingness to sign a written informed consent. 14\. Willing and able to comply with the requirements and restrictions in this protocol. 15\. Patients who have received the vector, protein subunit, or nucleic acid COVID-19 vaccines are eligible to enroll. Exclusion Criteria: 1. Prior liver transplant. 2. Known human immunodeficiency virus (HIV) positive (testing not required). 3. Use of any live vaccines against infectious diseases within 28 days of first dose of study drug administration. 4. History of trauma or major surgery within 28 days prior to the first dose of study drug administration. (Tumor biopsy or placemen