This is an open label, multi-center, phase 1 study of BBI608 and BBI503 administered orally in combination to patients with advanced solid tumors. The primary goal is to determine the safety, tolerability, and recommended phase II dose (RP2D) of the combination regimen.

Inclusion Criteria

1. Signed written informed consent must be obtained and documented according to International Conference on Harmonisation (ICH) and local regulatory requirements

2. A histologically or cytologically confirmed solid tumor that is metastatic, unresectable, or recurrent and for which standard therapies do not exist or are no longer effective

   a. Patients must not be considered eligible for a potentially curative resection

3. ≥ 18 years of age

4. Measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1

5. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1

6. 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 dose

7. Females of childbearing potential must have a negative serum pregnancy test

8. Aspartate transaminase (AST) < 2.5 x upper limit of normal (ULN) and alanine transaminase (ALT) ≤ 2.5 × ULN.

   1. Patients who do not have hepatocellular carcinoma but who have liver lesions or liver metastases may be eligible if they have AST < 3.5 x ULN and AST < 3.5 x ULN if agreed upon by the investigator and medical monitor for the sponsor.
   2. Patients with hepatocellular carcinoma may be eligible provided they have AST and ALT that are ≤ 5.0 x ULN.

9. Hemoglobin (Hgb) ≥ 9 g/dL

10. Total bilirubin ≤ 1.5 × ULN. Patients with liver lesions who do not have hepatocellular carcinoma and who have a total bilirubin ≤ 2.0 x ULN may be eligible if agreed upon by the investigator and medical monitor for the sponsor.

    1. Patients with hepatocellular carcinoma may be eligible provided they have total bilirubin ≤ 3.0 x ULN and are considered Child-Pugh Class A or Child-Pugh Class B7 (Child-Pugh Class B with a total Child-Pugh score not to exceed 7).
    2. Patients with Gilbert's syndrome uncomplicated by other liver disease may be eligible if agreed upon by the investigator and medical monitor for the sponsor.

11. Creatinine ≤ 1.5 × ULN or, for patients with creatinine levels above institutional upper limit of normal, creatinine clearance must be > 60 mL/min/1.73 m^2.

12. Absolute neutrophil count ≥ 1.5 x 10^9/L

13. Platelets ≥ 100 x 10^9/L; patients with hepatocellular carcinoma may enroll provided they have a platelet count ≥ 75 x 10^9/L.

14. Life expectancy ≥ 3 months

Exclusion Criteria

1. Anti-cancer chemotherapy, radiotherapy, immunotherapy, or investigational agents within 7 days of first dose of BBI608 and BBI503. Patients may begin BBI608 and BBI503 on a date determined by the investigator and medical monitor for the sponsor after a minimum of 7 days since last receiving anti-cancer treatment, provided that all treatment-related adverse effects have resolved or have been deemed irreversible

2. Surgery within 4 weeks prior to first dose

3. Any known untreated brain metastases. Treated subjects must be stable 4 weeks after completion of treatment for brain metastases and image documented stability is required. Patients must have no clinical symptoms from brain metastases and must be either off of 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

4. Pregnant or breastfeeding

5. Significant gastrointestinal disorder(s) (e.g., active Crohn's disease or ulcerative colitis, or a history of extensive gastric resection and/or small intestinal resection) such that absorption of oral medications is impaired.

6. Unable or unwilling to swallow BBI608 and/or BBI503 capsules daily

7. Prior treatment with either BBI608 or BBI503

8. Uncontrolled concurrent 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 on mild exertion), uncontrolled infection or psychiatric illness/social situations that would limit compliance with study requirements

9. Subjects with a history of another primary cancer, with the exception of: a) curatively resected non-melanoma skin cancer; b) curatively treated cervical carcinoma in situ; and c) other primary solid tumors (with no known active disease present) that, in the opinion of the investigator, will not affect patient outcome in the setting of the current diagnosis

   1. Patients with adenocarcinoma of unknown primary are excluded
   2. Patients with a diagnosis of two co-existing primary cancers are excluded

10. Abnormal ECGs that are clinically significant such as QT prolongation (QTc > 480 msec), clinically significant cardiac enlargement or hypertrophy, new bundle branch block or existing left bundle branch block, or signs of new, active ischemia a. 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