Domvanalimab and Zimberelimab in Advanced Liver Cancers

Inclusion Criteria: 1. Patient must have a histologically confirmed diagnosis consistent with HCC or bile duct cancer (including intrahepatic cholangiocarcinoma, extrahepatic cholangiocarcinoma, and gall bladder cancers); known fibrolamellar HCC, or combined HCC-cholangiocarcinoma will be excluded. 2. Locally advanced or metastatic disease * 2a. 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. * 2b. Measurable disease, as defined as lesions that can accurately be measured in at east 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 toxicity are not eligible. 4. Availability of recent formalin-fixed, paraffin-embedded (FFPE) tumor tissue block or slides in which the biopsy or resection was performed within 3 years. Baseline tissue can be obtained after consent but must be prior to initiation of zimberelimab and domvanalimab. It is strongly recommended that tissue is obtained from 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 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% 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 B7-8 (only 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: * 9a. Platelet count ≥ 50,000/mm\^3 * 9b. Hgb ≥ 8.5 g/dl * 9c. Absolute neutrophil ≥ 1,000 cells/mm\^3 * 9d. Total bilirubin ≤ 3.0 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, and such patients may be enrolled based in consultation with the principal investigator). * 9e. INR ≤ 2 * 9f. AST, ALT ≤5 times ULN * 9g. Calculated creatinine clearance (CrCl) ≥ 40 mL/min. CrCl can be calculated using the Cockroft-Gault method. * 9h. 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 adequate contraception (hormonal or barrier method of birth control; abstinence) 4 weeks prior to study entry, for the duration of study participation, and for 120 days after the last dose of zimberelimab or domvanalimab. See contraception guidelines in Appendix 1. 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 within 72 hours prior to receiving the first dose of study medication 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 or HBV viral load must be less than 100 IU/mL prior to first dose of study drug. Subjects on active HBV therapy with viral loads under 100 IU/ml should stay on the same therapy throughout study treatment. 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. In addition, subjects with successful HCV treatment are allowed as long as there are ≥4 weeks between completion of HCV therapy and start of study drug. Successful HCV treatment definition: SVR12. 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 placement of central venous access catheter (eg, port or similar) is not considered a major surgical procedure). 5. Underlying medical conditions that, in the investigator's opinion, will make the administration of study drugs hazardous, including but not limited to: * 5a. Interstitial lung disease, including history of interstitial lung disease or non infectious pneumonitis (lymphangitic spread of cancer is not disqualifying), * 5b. Active viral, bacterial, or fungal infections requiring parenteral treatment within 14 days of the initiation of study drugs, * 5c. Clinically significant cardiovascular disease, * 5d. A condition that may obscure the interpretation of toxicity determination or AEs, * 5e. History of prior solid-organ transplantation. 6. Hypersensitivity to IV contrast; not suitable for pre-medication. 7. Pre-existing thyroid abnormality with thyroid function that cannot be maintained in the normal range with medication. 8. Any active autoimmune disease or a documented history of autoimmune disease or syndrome that required systemic treatment in the past 2 years (ie, with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs), except for vitiligo or resolved childhood asthma/atopy. * 8a. Replacement therapy (eg, thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment. * 8b. Participants with asthma who require intermittent use of bronchodilators, inhaled corticosteroids, or local corticosteroid injections will not be excluded from this study. Participants on chronic systemic corticosteroids will be excluded from the study. 9. Known history of active bacillus tuberculosis. 10. Subjects with a condition requiring systemic treatment with either corticosteroids (\> 10 mg/day prednisone equivalent) or other immunosuppressive medications within 14 days of study administration. Inhaled or topical steroids and adrenal replacement doses ≤10 mg/day prednisone equivalents are permitted in the absence of autoimmune disease. 11. Known severe hypersensitivity reactions to monoclonal antibodies (≥Grade 3). 12. Prior malignancy active within the previous 2 years except for locally curable cancers that have been apparently cured, such as basal or squamous cell skin cancer, superficial bladder cancer, or carcinoma in situ of the cervix, breast, or prostate cancer. 13. Prisoners or subjects who are involuntarily incarcerated. 14. If a participant has symptomatic or clinically active brain metastases including leptomeningeal disease, they must be excluded if: * Has evidence of progression by neurologic symptoms * Has metastatic brain lesions that require immediate intervention. * Has carcinomatous meningitis, regardless of clinical stability 15. Pregnant or nursing (lactating) women, where pregnancy is defined as the state of a female after contraception and until the termination of gestation, confirmed by a positive hCG laboratory test. 16. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. 17. Has significant dementia or other mental condition that precludes the participant's ability to consent to the study. 18. Use of other investigational drugs (drugs not marketed for any indication) within 28 days or 5 half-lives (whichever is longer) of first dose of study drugs. 19. Known hypersensitivity to recombinant proteins, or any excipient contained in the study drug formulations.