Patients must have Barcelona Clinic Liver Cancer (BCLC) stage: intermediate (B) or advanced (C) within days prior to study entry Stage B (not applicable for transarterial chemoembolization [TACE]), or stage C based on Barcelona Clinic Liver Cancer (BCLC) staging system Barcelona Clinic Liver Cancer (BCLC) stage B (that is not eligible for locoregional therapy) or stage C Disease not amenable to curative or transplant surgery ([Barcelona Clinic Liver Cancer [BCLC] Stage B); disease must be reviewed by members of disease management team at the local enrolling institution and be amenable to deb-TACE to treat all sites of disease in one session; for the dose escalation, regional lymphadenopathy and sub-centimeter pulmonary nodules are allowed as well as segmental portal vein involvement Intermediate stage HCC (Barcelona Clinic Liver Cancer [BCLC] class B), not eligible for curative treatment, but with Child-Pugh A or B; additionally, tumor cannot involve greater than % of the entire liver Barcelona Clinic Liver Cancer (BCLC) D = patients with distant metastasis Have Barcelona Clinic Liver Cancer (BCLC) stage C disease or BCLC stage B disease not amenable to locoregional therapy or refractory to locoregional therapy, and not amenable to a curative treatment approach Barcelona Clinic Liver Cancer stage B or C; segmental and subsegmental portal vein thrombosis is allowed Patients will be staged according to the Barcelona Clinic Liver Cancer (BCLC) criteria Advanced stage HCC (Barcelona Clinic Liver Cancer [BCLC] Stage C or B per American Association for the Study of Liver Disease [AASLD] guidelines) Barcelona Clinic Liver Cancer (BCLC) Stage B or C disease not amenable to or progressing after loco-regional therapy and not amenable to a curative treatment approach Barcelona Clinic Liver Cancer (BCLC) stage B or C that cannot benefit from treatments of established efficacy such as resection, local ablation, chemoembolization. Has Barcelona Clinic Liver Cancer (BCLC) Stage C disease, or BCLC Stage B disease not amenable to locoregional therapy or refractory to locoregional therapy, and not amenable to a curative treatment approach. Barcelona Clinic Liver Cancer (BCLC) Stage C disease (Llovet et al ), or BCLC Stage B disease. Has Barcelona Clinic Liver Cancer (BCLC) Stage C disease or BCLC Stage B disease not amenable to locoregional therapy or refractory to locoregional therapy, and not amenable to a curative treatment approach Subjects categorized to stage B (not applicable for transarterial chemoembolization [TACE]) or stage C based on Barcelona Clinic Liver Cancer (BCLC) staging system Subject has BCLC stage B or C. Patients who are categorized under Barcelona-Cl?nic Liver Cancer (BCLC)-C stage Barcelona Clinical Liver Cancer Classification (BCLC) B or C Barcelona Clinic Liver Cancer (BCLC) stage C, and those with BCLC-B stage who cannot tolerate or failed transarterial chemoembolization (TACE) Barcelona Clinic Liver Cancer stage Category B or C that cannot benefit from treatments of established efficacy with higher priority such as resection, local ablation, chemoembolization or systemic sorafenib. Subject has unresectable stage B (intermediate), or C (advanced) Hepatocellular carcinoma according to the Barcelona Clinic Liver Cancer staging.Stage B subjects must have progressed after, or are not eligible for curative resection, transplantation, embolic, or ablative therapies Barcelona Clinic Liver Cancer (BCLC) advanced stage (C) hepatocellular carcinoma, or BCLC intermediate stage (B) hepatocellular carcinoma if treatment with transarterial chemoembolization is not considered appropriate Barcelona Clinic Liver Cancer (BCLC) stage B Barcelona Clinic Liver Cancer (BCLC) Stage C disease or BCLC Stage B disease not amenable to locoregional therapy or refractory to locoregional therapy. Subjects must be classified as TNM stage I, II, or III; alternatively, subjects may be classified as Barcelona Clinic Liver Cancer (BCLC) stage A or B