TSR-022 (Anti-TIM-3 Antibody) and TSR-042 (Anti-PD-1 Antibody) in Patients With Liver Cancer

Inclusion Criteria: * Histologically or cytologically confirmed hepatocellular cancer * Barcelona Clinic Liver Cancer Stage B or C * Cirrhosis grade of Child-Pugh class A or B7 * Subjects with HBV infection are required to be receiving effective antiviral therapy and have a viral load less than 100 IU/mL. Antiviral therapy is not required for subjects with HCV infection * Have at least one tumor lesion that can be accurately measured according to Response Evaluation Criteria in Solid Tumor (RECIST v1.1) * No prior systemic therapy for HCC * Age ≥ 18 years * ECOG performance status 0-1 * Resolved acute effects of any prior therapy to baseline or Grade ≤1 NCI CTCAE * Have adequate hematologic function as documented by ANC ≥ 1000/μcl, platelet count ≥ 60,000/μcl, and hemoglobin ≥ 8.5 mg/dl * Have adequate renal function as determined by a measured or calculated creatinine clearance ≥ 40 mL/min using the Cockcroft-Gault formula * Have adequate hepatic function, as documented by ALT and AST ≤5x upper limit of normal, total bilirubin ≤3 mg/dL, and albumin ≥2.8 g/dL * International normalized ratio (INR) or prothrombin time (PT) ≤2× ULN unless patient is receiving anticoagulant therapy as long as PT or partial thromboplastin (PTT) is within therapeutic range of intended use of anticoagulants * Prior local therapy, such as surgery, radioembolization, chemoembolization, or radiofrequency ablation is allowed if the index lesion(s) remains outside of the treatment field or has progressed since prior treatment * Participants must agree to not donate blood during the study or for 90 days after the last dose of protocol therapy * Female participant has a negative urine or serum pregnancy test within 7 days prior to taking study treatment if of childbearing potential and agrees to abstain from activities that could result in pregnancy from screening through 180 days after the last dose of study treatment, or is of nonchildbearing potential. * Participant must be able to understand the study procedures and agree to participate in the study by providing written informed consent. Exclusion Criteria: * Participant must not be simultaneously enrolled in any interventional clinical trial * Participant must not have had major surgery ≤ 3 weeks prior to initiating protocol therapy and participant must have recovered from any surgical effects * Participants must not have received investigational therapy ≤4 weeks, or within a time interval less than at least 5 half-lives of the investigational agent, whichever is shorter, prior to initiating protocol therapy. * Active or untreated central nervous system (CNS) and leptomeningeal metastases are excluded * Prior therapy with any medication targeting PD-1, PD-L1, or TIM-3 * Participant must not have a known hypersensitivity to TSR-042 and TSR-022 components or excipients. * Participants with active malignancy (other than HCC) or a prior malignancy within the past 2 years are excluded. Participants with completely resected cutaneous melanoma (early stage), basal cell carcinoma, cutaneous squamous cell carcinoma, cervical carcinoma in-situ, breast carcinoma in-situ, and localized prostate cancer are eligible * Participant must not have serious, uncontrolled medical disorder, or nonmalignant systemic disease. Examples include, but are not limited to uncontrolled ventricular arrhythmia, uncontrolled major seizure disorder, unstable spinal cord compression, or superior vena cava syndrome. * Unstable angina, new onset angina within last 3 months, myocardial infarction within last 6 months and current congestive heart failure New York Heart Association Class II or higher * Known history of Human Immunodeficiency Virus (HIV) infection * Active tuberculosis infection or other microbial infection or any active systemic infection requiring parenteral antibiotic therapy. All prior infections must have resolved following optimal therapy. * Participant has an active autoimmune disease that has required systemic treatment in the past 2 years (.ie., with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * History of idiopathic pulmonary fibrosis, interstitial lung disease, bronchial asthma, organizing pneumonia, bronchiolitis obliterans, drug-induced pneumonitis, or idiopathic pneumonitis * History of organ transplantation including allogeneic bone marrow transplantation * Participant has a diagnosis of immunodeficiency or has receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to initiating protocol therapy. * Participant has received a live vaccine within 7 days of initiating protocol therapy. * Psychiatric illness/social situations that would limit compliance with study requirements * Pregnant, lactating, breastfeeding, or intending to become pregnant during the study and for 180 days after the study