The purpose of this study is to evaluate rising dose levels of VS-5584 administered in combination with a fixed dose of VS-6063 in subjects with relapsed malignant mesothelioma to determine a recommended Phase 2 dose (RP2D) for further development of this combination in this indication.

This study is comprised of 2 sequential parts: Part 1 (Dose Escalation of VS-5584) and Part 2 (Expansion). Up to 56 evaluable subjects (i.e., subjects who complete at least 1 cycle [21 days] of therapy) will be enrolled, assuming that:

• Up to 6 dose levels of VS-5584 are studied in Part 1 (Dose Escalation of VS-5584) in combination with a fixed dose of VS-6063 at 400 mg twice daily (BID) with a maximum of 6 subjects enrolled per VS-5584 dose level, for a total of up to 36 subjects (exclusive of replacement subjects).
• Up to an additional 20 evaluable subjects may be enrolled in Part 2, the expansion portion of the study. Subjects will be treated with VS-5584 at the RP2D and schedule determined in the dose escalation portion of the study in combination with a fixed dose of VS-6063.

Inclusion Criteria:

1. Histopathologically-confirmed diagnosis of malignant mesothelioma (pleural or peritoneal). Must have disease that has relapsed following at least one prior line of chemotherapy.
2. Must have received at least 3 cycles of first-line chemotherapy.
3. Evaluable or measurable disease as assessed by Response Evaluation Criteria in Solid Tumors (RECIST).
4. Must have archival tumor tissue available for biomarker analysis. A study-specific tumor core biopsy, pleural effusion or ascites sample must be obtained prior to treatment if archival tissue is not available.
5. Performance status according to the Karnofsky Performance Scale ≥70%.
6. Fasting blood glucose of ≤ 140 mg/dL (7.8 mmol/L).
7. Adequate renal function (creatinine ≤ 1.5x upper limit of normal [ULN]) and/or glomerular filtration rate (GFR) of ≥50 mL/min.
8. Adequate hepatic function (total bilirubin ≤ 1.5x ULN; AST and ALT ≤ 3x ULN).
9. Adequate bone marrow function (hemoglobin ≥9.0 g/dL; platelets ≥100 x10^9 cells/L; absolute neutrophil count ≥1.5x10^9 cells/L) without the use of hematopoietic growth factors.

Exclusion Criteria:

1. Have had a previous extra pleural pneumonectomy (EPP).
2. Gastrointestinal condition which could interfere with the swallowing or absorption of study drug.
3. Uncontrolled or severe concurrent medical condition (including uncontrolled brain metastases).
4. Known history of stroke or cerebrovascular accident within 6 months prior to the first dose of study drug.
5. Any evidence of serious active infection.
6. Undergoing active treatment for a secondary malignancy.
7. Cancer-directed therapy (chemotherapy, radiotherapy) within 21 days of the first dose of study drug or 5 half-lives, whichever is shorter.
8. Major surgery within 28 days prior to the first dose of study drug.
9. Acute or chronic pancreatitis.
10. Diabetes mellitus requiring insulin treatment or subjects with a hemoglobin A1C (HbA1C) >7%.
11. History or evidence of cardiac risk.
12. Known history of malignant hypertension.