A Study of BBI503 in Adult Patients With Advanced Gastrointestinal Stromal Tumors

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 gastrointestinal stromal tumor that is metastatic, unresectable, or recurrent; and for which no currently approved, standard anti-cancer treatment option is available. * ≥ 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 * Alanine transaminase (ALT) ≤ 2.5 x the upper limit of normal (ULN), or ≤ 3.5 x ULN in the presence of primary or metastatic hepatic lesions * Hemoglobin (Hgb) ≥ 10 g/dl * Total bilirubin ≤ 1.5 x ULN * Creatinine ≤ 1.5 x ULN or creatinine clearance \> 50 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal. * Absolute neutrophil count ≥ 1.5 x 10\^9/L * Platelets ≥ 100 x 10\^9/L * PT ≤ 16 seconds and PTT ≤ 1.5 x ULN * Life expectancy ≥ 3 months * A patient with gastrointestinal stromal tumor (GIST) must also meet the following criteria: * Must have either positive immunostaining for the CD117-antigen, or contain a GIST associated KIT or PDGFR-α mutation. * Must have disease which is metastatic or locally advanced and unresectable * Must have received prior treatment with imatinib and sunitinib, and must have had disease progression during treatment with these agents, have had documented intolerance to these agents, or not be candidates for treatment with these agents. * Must have also failed or not be eligible for treatment with regorafenib. 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 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. Post-treatment image documentation of stability is required within 4 months of starting on study. 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 Principal Investigator, (e.g., Crohn's disease, ulcerative colitis, extensive gastric and small intestine resection) * 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). * Patients with a history of malignancies other than the tumor of interest except: adequately treated non-melanoma skin cancer, curatively treated in-situ cancer of the cervix, or other solid tumors curatively treated with no evidence of disease for \> 3 years. * 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.