Inclusion Criteria:

1. Signed written informed consent must be obtained and documented according to
International Conference on Harmonization (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

2. A histologically or cytologically confirmed ovarian, breast, non-small cell lung,
melanoma, head/neck, gastric/GEJ or other type of advanced cancer that is metastatic,
unresectable, or recurrent and for which weekly paclitaxel is an acceptable
therapeutic option

3. ≥ 18 years of age

4. Measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST
1.1, see Section 9)

5. Karnofsky performance Status ≥ 70% (Section 15)

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
BBI608 dose

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

8. Aspartate transaminase (AST) and alanine transaminase (ALT) £1.5 × upper limit of
normal (ULN), or ≤ 2.5 × ULN with metastatic liver disease

9. Hemoglobin (Hgb) ≥ 10 g/dl

10. Total bilirubin £ 1.5 × ULN

11. Creatinine £ 1.5 ´ ULN or creatinine clearance > 60 mL/min/1.73 m2 for patients with
creatinine levels above institutional normal

12. Absolute neutrophil count ³ 1.5 x 109/L

13. Platelets ≥ 100 x 109/L

14. Life expectancy ≥ 3 months

Exclusion Criteria:

1. Anti-cancer chemotherapy, radiotherapy, immunotherapy, or investigational agents
within four weeks of first dose with the exception for a single dose radiation up to
8 Gray (equal to 800 RAD) with palliative intent for pain control up to 14 days
before beginning the administration of BBI608

2. Surgery within 4 weeks prior to first dose

3. Any known symptomatic brain metastases requiring steroids. Patients with treated
brain metastases must be stable for 4 weeks after completion of that treatment, with
image documentation required. 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

4. Pregnant or breastfeeding

5. Significant gastrointestinal disorder(s), in the opinion of the Principal
Investigator, (e.g., Crohn's disease, ulcerative colitis, extensive gastric and small
intestine resection)

6. Unable or unwilling to swallow BBI608 capsules daily

7. 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

8. Known severe hypersensitivity to paclitaxel