A Study of BBI503 in Adult Patients With Advanced Hepatobiliary Cancer

Inclusion Criteria: * Signed written informed consent must be obtained and documented according to International Conference on Harmonisation (ICH) - Good Clinical Practice (GCP), the local regulatory requirements, and permission to use private health information in accordance with the Health Insurance Portability and Accountability Act (HIPPA) prior to study-specific screening procedures * Histologically or cytologically confirmed hepatocellular carcinoma or cholangiocarcinoma, that is metastatic, unresectable, or recurrent; and for which no currently approved, standard anti-cancer treatment option is available. Patients must have received standard of care treatment prior to enrollment. * ≥ 18 years of age * Measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Male or female patients of child-producing potential must agree to use contraception or avoidance of pregnancy measures during the study and for 30 days after the last BBI503 dose * Females of childbearing potential must have a negative serum pregnancy test * Aspartate transaminase (AST) and Alanine transaminase (ALT) ≤ 5.0x the upper limit of normal (ULN) * Hemoglobin \> 8.0 g/dL * Total bilirubin ≤ 2.5 x ULN * Creatinine ≤ 1.5 x ULN or creatinine clearance \> 50 mL/min according to the Cockcroft-Gault estimation. * Absolute neutrophil count ≥ 1.5 x 10\^9/L * Platelets ≥ 60 x 10\^9/L * Life expectancy ≥ 3 months * A patient with hepatocellular carcinoma (HCC) which has arisen out of any medical context must also meet the following criteria: * Must not be a candidate for potentially curative resection * Must be Child-Pugh class A or B7 (i.e., in order to be eligible, the total Child-Pugh score for a patient must be ≤ 7) * Must have received prior treatment with sorafenib; and have had either disease progression during treatment or have had documented intolerance to sorafenib such that further treatment with sorafenib is not possible. * Patients with uncontrolled massive ascites or presence of hepatic encephalopathy within four (4) weeks of first dose are excluded * A patient with confirmed cholangiocarcinoma of any type must also meet the following criteria: * Must have disease which is not amenable to surgical, radiation, or combined modality therapy with curative intent * Must have received prior treatment with gemcitabine, either alone or in combination with a platinum agent. Patients who are not eligible for gemcitabine must have received an alternate first-line systemic chemotherapy regimen Exclusion Criteria: * Anti-cancer chemotherapy, radiotherapy, immunotherapy, or investigational agents within 7 days of first dose of BBI503. Patients may begin BBI503 on a date determined by the investigator and medical monitor for the sponsor provided there is a minimum of 7 days since last receiving anti-cancer treatment, and that all prior treatment-related adverse events (AEs) have resolved or have been deemed irreversible. * Major surgery within 4 weeks prior to first dose (requiring general anesthesia and/or inpatient hospitalization for recovery). * Any known symptomatic or untreated brain metastases requiring increase of steroid dose within 2 weeks prior to starting on study. Patients with treated brain metastases must be stable for 4 weeks after completion of that treatment. Patients must have no clinical symptoms from brain metastases and must be either off steroids or on a stable dose of steroids for at least 2 weeks prior to protocol enrollment. Patients with known leptomeningeal metastases are excluded, even if treated. * Pregnant or breastfeeding * Significant gastrointestinal disorder(s), in the opinion of the treating investigator, (e.g., Crohn's disease, ulcerative colitis, extensive gastric and small intestine resection); such that absorption of oral medications may be impaired. * Unable or unwilling to swallow BBI503 capsules daily * Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, clinically significant non-healing or healing wounds, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, significant pulmonary disease (shortness of breath at rest or mild exertion), uncontrolled infection or psychiatric illness/social situations that would limit compliance with study requirements (e.g. no reliable transportation). * Subjects with history of another primary cancer, with the exception of: a) curatively resected non-melanoma skin cancer; b) curatively treated cervical carcinoma in situ; or c) other primary solid tumor with no known active disease present in the opinion of the investigator will not affect patient outcome in the setting of current hepatobiliary malignancy. * Abnormal ECGs which are clinically significant such as QT prolongation - QTc \> 480 msec, clinically significant cardiac enlargement or hypertrophy, new bundle branch block, or signs of active ischemia. Patients with evidence of prior infarction who are New York Heart Association (NYHA) functional class II, III, or IV are excluded, as are patients with marked arrhythmia such as Wolff Parkinson White pattern or complete atrioventricular (AV) dissociation.