This is an open-label, multicenter, phase 1 dose escalation study of BBI503 monotherapy, or BBI503 in combination with Sorafenib. This study population is adult patients with advanced solid tumors in monotherapy, or adult patients with advanced hepatocellular carcinoma in combination therapy.

Inclusion Criteria:

• Provision of written informed consent.
• ≥ 20 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
• Adequate organ function
• Life expectancy ≥ 3 months

Exclusion Criteria:

• Any known symptomatic or untreated brain metastases
• Pregnant or breastfeeding
• Crohn's disease, ulcerative colitis extensive gastric and small intestine resection
• Unable or unwilling to swallow BBI503 daily
• Uncontrolled concurrent disease
• Received other investigational drugs within 4 weeks prior to first dose
• Prior treatment with BBI503