Safety/Efficacy Study of LDE225 (Sonidegib) Plus Bortezomib in Patients With Relapsed or Relapsed/Refractory Multiple Myeloma

Inclusion Criteria: 1. Patients must have measurable MM requiring systemic therapy defined as at least one of the following: * Serum M-protein ≥ 0.5 g/dL * Urine M-protein ≥ 200 mg/24 hrs * Serum free light chain assay: involved free light chain level ≥ 10 mg/dL provided the serum free light chain ratio is abnormal 2. Must have progressed during or after at least two previous treatment regimens. Patients who have received previous high dose therapy or autologous stem cell transplantation are eligible. 3. ECOG Performance Status score of 0-2. 4. Patients with adequate bone marrow, liver and renal function. 5. Patient is able to swallow and retain oral medication. 6. QTcF ≤450 msec for males and ≤ 470 msec for females on the screening ECG. 7. Female patients must not be of childbearing potential or must agree to use adequate contraceptive measures. 8. Male patients willing to use adequate contraceptive measures. 9. Willingness and ability to comply with study and follow-up procedures. 10. Ability to understand the nature of this study and give written informed consent. Exclusion Criteria: 1. Received any treatment for myeloma-directed treatment within 21 days. Localized radiation and dexamethasone must be completed within 7 days prior to study treatment 2. Refractory to bortezomib, defined as progression on or within 60 days of last bortezomib dose. 3. Received any investigational drug within 28 days or 5 half-lives (whichever is longer) prior to the first dose of LDE225. For other anti-neoplastic therapy (e.g., chemotherapy, targeted therapy or radiation), a minimum of 14 days between termination of the study drug and administration of LDE225 is required. 4. Patients who have previously been treated with systemic LDE225 or with other Hedgehog (Hh) pathway inhibitors. 5. Received major surgical procedures within 28 days of beginning study drug, or minor surgical procedures within 7 days. No waiting is required following port-a-cath placement. 6. Those who are pregnant or lactating. 7. Patients with concurrent uncontrolled medical conditions that may interfere with their participation in the study or potentially affect the interpretation of the study data. 8. Patients with \> Grade 2 peripheral neuropathy (per NCI CTCAE V4.0) within 14 days prior to study enrollment. 9. Patients with a presence of active gastrointestinal disease or other condition that will interfere significantly with the absorption, distribution, metabolism, or excretion of oral therapy (e.g. ulcerative disease, uncontrolled nausea, vomiting, diarrhea Grade ≥2, and malabsorption syndrome). 10. Patients who have neuromuscular disorders (e.g. inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis and spinal muscular atrophy) or are on concomitant treatment with drugs that are recognized to cause rhabdomyolysis, such as HMG CoA inhibitors (statins), clofibrate and gemfibrozil, and that cannot be discontinued at least 2 weeks prior to starting LDE225 treatment. If it is essential that the patient stays on a statin to control hyperlipidemia, only pravastatin may be used with extra caution. 11. Patients who are planning on embarking on a new strenuous exercise regimen after initiation of study treatment. Muscular activities, such as strenuous exercise, that can result in significant increases in plasma CK levels should be avoided while on LDE225 treatment. 12. Receiving treatment with medications known to be moderate and strong inhibitors or inducers of CYP3A4 or CYP3A5, drugs that are BCRP substrates, or drugs metabolized by CYP2B6 or CYP2C9 that have narrow therapeutic index, and that cannot be discontinued before starting treatment with LDE225. Medications that are strong CYP3A4 or CYP3A5 inhibitors should be discontinued at least 7 days prior to starting LDE225. Strong CYP3A4 or CYP3A5 inducers should be discontinued at least 2 weeks weeks weeks prior to starting treatment with LDE225. 13. Therapeutic doses of warfarin sodium or any other warfarin-derivative anticoagulants are not permitted since LDE225 is a competitive inhibitor of CYP2C9 based on the in vitro data. In this situation therapeutic anticoagulation may be accomplished using low molecular weight heparin (LMWH) or similar agents. 14. Those diagnosed with cardiac conditions currently or within last 6 months. 15. Those experiencing angina pectoris within 3 months. 16. Those who experienced acute myocardial infarction within 3 months. 17. Those with inadequately controlled hypertension defined as systolic blood pressure \[SBP\] \> 180 mmHg or diastolic blood pressure (DBP) \> 100 mmHg. Patients with values above these levels must have their blood pressure controlled with medication prior to starting treatment. Patients with a history of labile hypertension, or a history of poor compliance with an antihypertensive regimen are to be excluded. 18. Pregnant or lactating women, where pregnancy is confirmed by a positive human chorionic gonadotropin (hCG) laboratory test. 19. Patients who are not willing to apply highly effective contraception during the study and after the final dose of study treatment. 20. Sexually active males who are unwilling to use a condom during intercourse while taking drug and for 6 months after stopping investigational medications and agree not to father a child in this period. 21. Those with a serious active infection at the time of treatment, or another serious underlying medical condition that would impair the ability of the patient to receive protocol treatment. 22. Those presenting with other active cancers, or history of treatment for invasive cancer within 3 years. Patients with Stage I cancer who have received definitive local treatment and are considered unlikely to recur are eligible. All patients with previously treated in situ carcinoma (i.e., non-invasive) are eligible, as are patients with history of non-melanoma skin cancer. 23. Those with psychological, familial, sociological, or geographical conditions that do not permit compliance with the protocol.