This is an open label, multi-center, Phase 1/2 study of BBI608 administered in combination with immunotherapy in adult patients with advanced cancers. The goal of the study is to determine the RP2D of BBI608 in combination with each of the immunotherapeutic agents.

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 cancer that is metastatic, unresectable, or recurrent and for which treatment with ipilimumab, or nivolumab, or pembrolizumab is a reasonable therapeutic option in the opinion of the investigator.
3. ≥ 18 years of age
4. Measurable disease as defined by Immune-Related Response Evaluation Criteria in Solid Tumors (irRECIST).
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 × upper limit of normal (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.
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. Patients may begin BBI608 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 events (AEs) have resolved or have been deemed irreversible
2. Had a surgical procedure requiring general anesthesia or inpatient hospitalization for recovery less than 4 weeks prior to beginning protocol therapy.
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 have not required systemic corticosteroids >10 mg/day prednisone or equivalent for at least 2 weeks prior to first dose of study drug.
4. Pregnant or breastfeeding
5. Unable or unwilling to swallow BBI608 capsules daily
6. 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.
7. Has an active autoimmune disease requiring immunosuppression with the exception of subjects with isolated vitiligo, resolved childhood asthma or atopic dermatitis, controlled hypoadrenalism or hypopituitarism, and euthyroid patients with a history of Grave's disease.
8. Has interstitial lung disease or active, non-infectious pneumonitis
9. Has a transplanted organ or has undergone allogeneic bone marrow transplant
10. Has received a live vaccine within 30 days prior to first dose.
11. Known hypersensitivity to a component of protocol therapy
12. 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
13. 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; c) localized prostate cancer not requiring systemic therapy; and c) other primary tumors with no known active disease present that, in the opinion of the investigator and medical monitor for the sponsor, will not affect patient outcome in the setting of the current diagnosis.
14. 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.