Combined Treatment of Durvalumab, Bevacizumab, Tremelimumab and Transarterial Chemoembolization (TACE) in Subjects With Hepatocellular Carcinoma or Biliary Tract Carcinoma

Background: Hepatocellular carcinoma (HCC) is the fifth most common cancer in the world. Most people with advanced HCC survive an average of 6 to 9 months. Researchers are evaluating a combination of treatment drugs to delay the progression of HCC; aiming to help people with HCC live longer. Objective: To study the 6-month progression-free survival in people with advanced HCC treated with bevacizumab, durvalumab, and TACE. Eligibility: Adults ages 18 and older with intermediate or advanced HCC Design: Participants will be screened with a physical exam and medical history. They will have tests to evaluate their hearts as well as blood and urine. A CT and/or MRI scans will be done during the study. If a prior tumor sample is not available; participants may undergo a biopsy. They may undergo an endoscopy of their esophagus and stomach. Participants will get the study drugs in 21-day cycles: Two treatment drugs will be injected into a vein every 3 weeks. Patients will have an interventional treatment procedure done by interventional radiology under sedation; chemotherapy beads will be infused into artery branches in the liver. Participants may have to stay in the hospital for 24 hours for observation, after this procedure. This interventional procedure may be done more than once during the study. Participants may need to repeat some of the screening tests throughout the study. Participants may have to stop taking some of their cancer treatment drugs during the study. Participants will continue on the study until their cancer progresses or until the side effects of the treatment drugs are not tolerable.

* INCLUSION CRITERIA: * Participants must have * histopathological confirmation of HCC (Cohorts 1 and 3) OR * histopathological confirmation of BTC or histopathological confirmation of carcinoma in the setting of clinical and radiological characteristics which, together with the pathology, are highly suggestive of a diagnosis of BTC (Cohort 2). * Participants should have progressed on standard of care systemic therapy or been intolerant of or have refused standard treatment. Note: For participants enrolled in Cohort 3 (HCC, BCLC stage B), standard of care chemotherapy is not required prior to enrollment. * Participants must have disease that is not amenable to potentially curative resection, radiofrequency ablation, or liver transplantation * Participants must have evaluable or measurable disease per RECIST 1.1 * Participants must have at least one lesion accessible for TACE (Cohort 3) * Participants must have lesions accessible for biopsy and be willing to undergo pre- and posttreatment biopsies * ECOG performance status of 0 to 1 * If liver cirrhosis is present, patient must have a Child-Pugh score \ 100 mmHg), based on an average of 3 BP readings on 2 sessions. Note: anti-hypertensive therapy to achieve these parameters is allowable. * Prior history of hypertensive crisis or hypertensive encephalopathy * Significant vascular disease (e.g., aortic aneurysm requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior to initiation of study treatment * Evidence of bleeding diathesis or significant coagulopathy (with or without current therapeutic anticoagulation). * Recent (within 10 days of first dose of study treatment) use of aspirin * Thromboembolic event within 6 months of initiation of study treatment (including cerebrovascular accident (CVA) and myocardial infarction (MI). * History of hemoptysis (\>2.5 mL of bright red blood per episode) within 1 month prior to treatment initiation. * Serious, non-healing wound, active ulcer, or untreated bone fracture. * HIV-positive participants are excluded because HIV causes complicated immune deficiency and study treatment can pose more risks for these patients. * History of severe hypersensitivity reaction to any monoclonal antibody. * Congestive heart failure, transmural myocardial infarction, angina pectoris requiring medication, clinically significant valvular disease, high-risk arrhythmia within 12 months prior to treatment initiation. Prior history of hypertensive crisis or hypertensive encephalopathy. * Prior invasive malignancies within the past 5 years prior to treatment initiation (with the exception of non-melanoma skin cancers, non-invasive bladder cancer or localized prostate cancer for whom systemic therapy is not required) * Active or history of inflammatory bowel disease (colitis, Crohn s), irritable bowel disease, celiac disease, or other serious, chronic, gastrointestinal conditions associated with diarrhea. * History of abdominal fistula or gastrointestinal perforation within 6 months prior to initiation of study treatment. * History of chronic autoimmune disease (e.g., Addison s disease, multiple sclerosis, Graves disease, Hashimoto s thyroiditis, rheumatoid arthritis, hypophysitis, systemic lupus erythematosus, Wegener s granulomatosis, sarcoidosis syndrome etc.) or other connective tissue diseases with symptomatic disease within the 3 years of initiation of study treatment. Note: Active vitiligo or a history of vitiligo will not be a basis for exclusion. * Diverticulitis either active or history of within 2 years of initiation of study treatment. Note that diverticulosis is permitted. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection or psychiatric illness/social situations that may impair the patient s tolerance of study treatments. * Received any live vaccine within the last 30 days before treatment initiation. * Participants who have undergone prior liver transplantation. * Pregnant women are excluded from this study because durvalumab s and bevacizumab s potential for teratogenic or abortifacient effects is unknown. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with tremelimumab, durvalumab and bevacizumab, breastfeeding should be discontinued if the mother is treated with study drugs.