Study of ACY-1215 in Combination With Lenalidomide, and Dexamethasone in Multiple Myeloma

Inclusion Criteria: * Relapsed or Relapsed/Refractory MM with progressive disease (PD) according to IMWG. * Received at least 1 prior line of therapy for MM (Phase 1) * Secretory MM for which the patient previously received 1-3 prior lines of therapy (Phase 2). * Able to provide written consent * Not a candidate for autologous stem cell transplant (ASCT) or declined option. * ≥18 years of age * Karnofsky Performance Status score ≥ 70 * Adequate bone marrow reserve as evidenced by ANC \> 1.0x10\^9/L;Platelet \> 50x10\^9/L * Creatinine Clearance of ≥ 50 mL/min * Adequate hepatic function as evidenced by serum bilirubin values \< 2.0 mg/dL; ALT and/or AST \< 3xULN. * Corrected serum calcium ≤ ULN * Recovered from the effects of any prior systemic therapy or radiotherapy for Multiple Myeloma * Able to take acetylsalicylic acid (ASA) (81 or 325 mg) daily as prophylactic anticoagulation. Patients intolerant to ASA may use low molecular weight heparin. Lovenox is recommended. Coumadin will be allowed provided the patient is fully anticoagulated, with an INR of 2 or 3. * Agreement to participate in RevAssist® Program * Female of childbearing potential must have a negative serum or urinary pregnancy test with a sensitivity of at least 50 mIU/mL 10-14 days prior to and again within 24 hours of prescribing lenalidomide for Cycle 1 and must either commit to continued abstinence or begin TWO acceptable methods of birth control, one highly effective method and one additional effective method at the same time, at least 28 days prior to taking lenalidomide. Also agree to ongoing pregnancy testing. * If male, including those who have had a vasectomy, must agree to use a latex condom during any sexual contact with a female of childbearing potential. Exclusion Criteria: * Received any of the following antitumor therapies * Radiotherapy or systemic therapy within 2 weeks of Cycle 1 Day 1 (C1D1) * Investigational or biologic therapies within 3 weeks of C1D1 * Prior peripheral ASCT within 12 weeks of C1D1 * Prior allogeneic stem cell transplant * Prior treatment with a histone deacetylase (HDAC) inhibitor * Presence of an active systemic infection requiring treatment. * History of other malignancies unless a.) the patient has undergone definitive treatment more than 5 years prior and is without evidence of recurrent malignant disease or b.) had basal or squamous cell carcinoma of the skin; superficial carcinoma of the bladder; carcinoma of the prostate with current prostat specific antigen \< 0.1 ng/mL; ductal carcinoma in situ; or cervical intraepithelial neoplasia. * Known or suspected human immunodeficiency virus (HIV), hepatitis B surface antigen-positive status or known or suspected active hepatitis C infection. * If female, is lactating. * History of significant cardiovascular, neurological, endocrine, gastrointestinal, respiratory, or inflammatory illness that could preclude study participation, pose an undue medical hazard, or interfere with the interpretation of the study results, including but not limited to congestive heart failure (NYHA Class 3 or 4), unstable angina; cardiac arrhythmia, recent (within past 6 months) myocardial infarction or stroke; uncontrolled hypertension; diabetes mellitus with \>2 episodes of ketoacidosis in the preceding 12 months, COPD requiring \>2 hospitalizations in preceding 12 months * QTcF \> 480 msec, family or personal history of long QTc syndrome or ventricular bigeminy; previous history of drug-induced QTc prolongation or the need for medications known or suspected of producing prolonged QTc intervals on ECG * Current enrollment in another clinical trial involving treatment and/or is receiving an investigational agent for any reason * Documented plasma cell leukemia or known amyloidosis. (Plasma cell leukemia is defined as the presence of \>20% plasma cells in the peripheral blood and an absolute plasma cell count of ≥2000 muL * Known hypersensitivity to thalidomide or lenalidomide. * History of erythema nodosum characterized by desquamating rash while taking thalidomide or similar drugs. * Non-secretory or oligo-secretory Multiple Myeloma (Phase II only; such disease is permissible in Phase I).