Known fibrolamellar HCC, sarcomatoid HCC, or mixed cholangiocarcinoma and HCC Histologically confirmed diagnosis of hepatocellular carcinoma (mixed HCC/cholangiocarcinoma is allowed) Patient must have a histologically confirmed diagnosis hepatocellular carcinoma; known fibrolamellar HCC, sarcomatoid HCC or mixed cholangiocarcinoma and HCC will be excluded Progressed on, be intolerant of, or refused sorafenib (for hepatocellular carcinoma [HCC]), second line treatment and beyond for cholangiocarcinoma or gemcitabine-based chemotherapy for biliary tract cancer. Known fibrolamellar HCC, sarcomatoid HCC, or mixed cholangiocarcinoma and HCC. Known fibrolamellar or mixed HCC-cholangiocarcinoma histology Fibrolamellar carcinoma or mixed HCC Pathologic diagnosis of hepatocellular carcinoma (including fibrolamellar variants and biphenotypic tumors with a hepatocellular carcinoma [HCC] component) Patient must have advanced hepatocellular carcinoma; fibrolamellar HCC is not allowed; hepatocellular carcinoma should be confirmed by at least one of the following:\r\n* Tissue diagnosis\r\n* The presence of one or more liver lesions measuring >= cm in longest diameter, showing characteristic arterial enhancement and venous washout using arterial-phase contrast enhanced imaging, and a clinical history of cirrhosis Diagnosis of hepatocellular carcinoma, cholangiocarcinoma, or liver metastasis from any histology Part Group B is restricted to HCC (fibrolamellar and mixed hepatocellular/cholangiocarcinoma subtypes are not eligible). Histological diagnosis of cholangiocarcinoma, hepatocholangiocarcinoma, fibrolamellar carcinoma and hepatoblastoma Known fibrolamellar HCC, sarcomatoid HCC, or mixed cholangiocarcinoma and HCC histology Known fibrolamellar HCC, sarcomatoid HCC, or mixed cholangiocarcinoma and HCC Biliary tract cancers or fibrolamellar variant tumors are excluded\r\n* Cases with mixed, composite, or combined HCC-cholangiocarcinoma histology are eligible with approval from study chair and provided the treating investigator believes it is in the best interest of the patient to treat the tumor with therapy targeted towards the HCC component of tumor based upon review of pathology and clinical characteristics Patients with fibrolamellar HCC, cholangiocarcinoma, and combined HCC-cholangiocarcinoma Has a HCC diagnosis confirmed by radiology, histology or cytology (fibrolamellar and mixed hepatocellular/cholangiocarcinoma subtypes are not eligible). Must have histologically or cytologically confirmed diagnosis of HCC (fibrolamellar and mixed hepatocellular/cholangiocarcinoma subtypes are not eligible). Fibrolamellar carcinoma or mixed hepatocellular cholangiocarcinoma. Known fibrolamellar HCC, sarcomatoid HCC, or mixed cholangiocarcinoma and HCC Have known HCC with fibro-lamellar or mixed histology. cholangiocarcinoma For Cohort : has histologically or cytologically confirmed diagnosis of HCC (fibrolamellar and mixed hepatocellular/cholangiocarcinoma subtypes are not eligible) based on pathology report For Cohort : has an HCC diagnosis confirmed by radiology, histology, or cytology (fibrolamellar and mixed hepatocellular/cholangiocarcinoma subtypes are not eligible) Subject has fibrolamellar variant of HCC. Known fibrolamellar HCC, sarcomatoid HCC, or mixed cholangiocarcinoma and HCC Diagnosis of hepatocellular carcinoma (HCC) confirmed histologically, excluding mixed HCC histology (e.g. HCC plus cholangiocarcinoma) or fibrolamellar variant Histologically/cytologically verified, non-resectable, recurrent, or metastatic biliary tract carcinoma including intrahepatic cholangiocarcinoma, extrahepatic cholangiocarcinoma and gallbladder carcinoma; combined cholangiocarcinoma and hepatocellular carcinoma is allowed Known HCC with fibro-lamellar or mixed histology Histologic diagnosis of liver-confined fibrolamellar or non-fibrolamellar hepatocellular carcinoma (HCC) Part B: Hepatocellular cancer (excluding fibrolamellar carcinoma) Diagnosis of fibrolamellar HCC or tumors of mixed histology. Fibrolamellar histology HCC, mixed hepatocholangiocarcinoma, hepatic sarcomas and other non-HCC primary liver tumors Fibrolamellar carcinoma or mixed hepatocellular cholangiocarcinoma Fibrolamellar carcinoma or mixed hepatocellular cholangiocarcinoma. Prior cholangiocarcinoma Patients with a diagnosis of hepatocellular carcinoma (HCC), intrahepatic cholangiocarcinoma, or metastatic liver cancer planned to receive definitive doses of radiation or surgical resection are eligible