Study of the Combination of Panobinostat and Carfilzomib in Patients With Relapsed/Refractory Multiple Myeloma

Inclusion Criteria: 1. Eligible participants must have multiple myeloma using standard criteria. 2. Patients must have measurable disease requiring systemic therapy defined as at least one of the following: * Serum M-protein ≥1 g/dl (≥10 g/l) * Urine M-protein ≥200 mg/24 hrs * Serum free light chain assay: involved free light chain level ≥10 mg/dl (≥100 mg/l) provided the serum free light chain ratio is abnormal 3. Must have progressed during or after at least one previous bortezomib-containing treatment regimen. Patients who have received previous high-dose therapy/autologous stem cell transplantation are eligible. 4. Eastern Cooperative Oncology Group (ECOG) performance status of 0-2. 5. Must meet the following laboratory criteria: * Absolute neutrophil count (ANC) ≥1000/μL; * Platelets ≥70,000/microL; * AST or ALT and alkaline phosphatase (ALP) must be ≤ 2.5 x ULN, or ≤ 5 x ULN in patients with plasmacytomas of the liver; * Total bilirubin ≤ 1.5 x the institutional ULN; * Serum creatinine ≤ 1.5 x ULN or calculated creatinine clearance ≥ 50 ml/min; * Serum potassium, calcium, magnesium WNL (These may be corrected prior to starting therapy, to make the patient eligible.) 6. Ability to swallow oral medications. 7. Baseline MUGA or ECHO must demonstrate left ventricular ejection fraction (LVEF) ≥ the lower limit of the institutional limits of normal. 8. Male or females ≥ 18 years of age. 9. Female patients must not be of child-bearing potential or must agree to use adequate contraceptive measures. 10. Male patients willing to use adequate contraceptive measures. 11. Willingness and ability to comply with the trial and follow-up procedures. 12. Ability to understand the nature of this trial and give written informed consent. Exclusion Criteria: 1. Currently receiving or have received systemic cancer therapy (chemotherapy, biologic therapy) ≤ 21 days of initiating study therapy. For patients receiving small molecule targeted therapy, study treatment may begin \>21 days after last dose or \>5 half lives of previous treatment, whichever is shorter. Patients must have completed radiation therapy ≥7 days prior to starting study treatment. Patients must have recovered from or come to a new chronic stable baseline from all treatment-related toxicities. Dexamethasone or other high-dose steroid therapy must be stopped ≥ days prior to starting study treatment. 2. Previous treatment with HDAC, DAC, HSP90 or valproic acid for treatment of cancer. 3. Requires valproic acid for any medical condition during the study ≤5 days prior to first panobinostat treatment. 4. Patient has not recovered from all therapy-related toxicities associated with prior treatments to \< Grade 2 CTCAE. 5. Known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib). 6. Patients with pleural effusions requiring thoracentesis or ascites requiring paracentesis ≤14 days prior to study entry. 7. Patients using medications that have a risk of prolonging the QT interval or inducing Torsade de Pointes if treatment cannot be discontinued or switched to a different medication prior to receiving study drug. 8. Patients with \> grade 2 diarrhea. 9. Patients with impaired cardiac function. 10. Infection requiring IV antibiotics. 11. Patients with \> grade 2 peripheral neuropathy or with uncontrolled pain. 12. Women who are pregnant or lactating. 13. Any concurrent medical illness that may impair the ability of the patient to tolerate study treatment and comply with the requirements of the study. 14. Mental condition that would prevent patient comprehension of the nature of, and risk associated with, the study. 15. Use of any non-approved or investigational agent ≤30 days prior to administration of the first dose of study drug. Patients may not receive any other investigational or anti-cancer treatments while participating in this study. 16. Presence of other active cancers, or history of treatment for invasive cancer ≤ 5 years. Patients with stage I cancer who have received definitive local treatment at least 3 years previously, 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.