Tremelimumab With Chemoembolization or Ablation for Liver Cancer

-INCLUSION CRITERIA: 1. Patients must have histopathological confirmation of hepatocellular carcinoma (HCC) or (Cohort E only) biliary tract carcinoma (BTC) by the Laboratory of Pathology of the National Cancer Institute (NCI) prior to entering this study 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 HCC (or biliary tract carcinoma in Cohort E). Fibrolammelar variant is also allowed. For cohort E, the term BTC includes intraor extrahepatic cholangiocarcinoma, gallbladder cancer or ampullary cancer, as long as there is an intrahepatic component amenable to radiofrequency ablation (RFA). 2. Patients must have disease that is not amenable to potentially curative resection, transplantation or ablation. For Cohorts A, C and D patients must have progressed on, been intolerant to, or refused prior sorafenib therapy. Cohort E patients must have received at least one line of chemotherapy for BTC. 3. Disease must be technically amenable to transhepatic arterial chemoembolization (TACE), radiofrequency ablation (RFA) or cryoablation. Each case will be discussed at gastrointestinal (GI) tumor board with interventional radiology. Patients must have evaluable disease. 4. If liver cirrhosis is present, patient must have a Child-Pugh A/B7 classification. 5. Age greater than or equal to 18 years 6. Life expectancy of greater than 3 months. 7. Eastern Cooperative Oncology Group (ECOG) performance status 0-2. 8. Patients must have normal organ and marrow function as defined below: * leukocytes greater than or equal to 3,000/mcL * absolute neutrophil count greater than or equal to 1,000/mcL * platelets greater than or equal to 60,000/mcL * total bilirubin, If cirrhosis present: Part of Child Pugh requirement. If no cirrhosis: Bili should be less than or equal to 2 times upper limit of normal (ULN) * Serum albumin, If cirrhosis present: Part of Child Pugh requirement. If no cirrhosis: albumin should be greater than or equal to 2.5g/dl * Patients are eligible with alanine aminotransferase (ALT) or aspartate aminotransferase (AST) up to 5 times ULN. * creatinine, less than 1.5 times institution upper limit of normal OR * creatinine clearance greater than or equal to 45 mL/min/1.73 m(2), as calculated below, for patients with creatinine levels above institutional normal 9. Patients must have recovered from any acute toxicity related to prior therapy, including surgery. Toxicity should be less than or equal to grade 1 or returned to baseline. 10. Patients must not have other invasive malignancies within the past 5 years (with the exception of non-melanoma skin cancers, non-invasive bladder cancer or localized prostate cancer for whom systemic therapy is not required). 11. Patient must be able to understand and willing to sign a written informed consent document. EXCLUSION CRITERIA: 1. Patients who have had standard of care chemotherapy, large field radiotherapy, or major surgery must wait 2 weeks prior to entering the study. For recent experimental therapies a 28 day period of time must elapse before treatment. 2. Patients who have undergone prior liver transplantation are ineligible. 3. Patients with known brain metastases will be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. 4. Uncontrolled intercurrent illness including, but not limited to, ongoing or active systemic infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia (excluding insignificant sinus bradycardia and sinus tachycardia) or psychiatric illness/social situations that would limit compliance with study requirements. 5. History of chronic autoimmune disease (e.g., Addison's disease, multiple sclerosis, Graves disease, Hashimoto's thyroiditis, rheumatoid arthritis, hypophysitis, etc.) with symptomatic disease within the 3 years before randomization. Note: Active vitiligo or a history of vitiligo will not be a basis for exclusion. 6. Dementia or significantly altered mental status that would prohibit the understanding or rendering of Information and Consent and compliance with the requirements of the protocol. 7. Diverticulitis (either active or history of) within the past 2 years. Note that diverticulosis is permitted. 8. Active or history of inflammatory bowel disease (colitis, Crohn's), irritable bowel disease, celiac disease, or other serious, chronic, gastrointestinal conditions associated with diarrhea. Active or history of systemic lupus erythematosus or Wegener's granulomatosis. 9. Currently receiving immunosuppressive doses of steroids or other immunosuppressive medications (inhaled and topical steroids are permitted) 10. History of sarcoidosis syndrome 11. Patients should not be vaccinated with live attenuated vaccines within 1 month of starting Tremelimumab treatment. 12 Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies) 13\. HIV-positive patients receiving anti-retroviral therapy are excluded from this study due to the possibility of pharmacokinetic interactions between antiretroviral medications and Tremelimumab. HIV positive patients not receiving antiretroviral therapy are excluded due to the possibility that Tremelimumab may worsen their condition and the likelihood that the underlying condition may obscure the attribution of adverse events. 14\. History of hypersensitivity reaction to human or mouse antibody products. 15\. Pregnancy and breast feeding are exclusion factors. The effects of Tremelimumab on the developing human fetus are unknown. Enrolled patients must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, the duration of study participation and 3 months after the end of the treatment. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. 16\. Patients with unhealed surgical wounds for more than 30 days.