Study to Determine the Maximum Tolerated Dose and Evaluate the Efficacy and Safety of CEP-18770 (Delanzomib) in Patients With Relapsed Multiple Myeloma Refractory to the Most Recent Therapy

Key Inclusion Criteria: The patient has: * relapsed multiple myeloma that has progressed following therapies that included bortezomib and an IMiD (thalidomide or lenalidomide) either alone or in any combination. * multiple myeloma, which is refractory to the most recent therapy (bortezomib or IMiD, or any other chemotherapy), or the patient did not tolerate and discontinued the most recent therapy for multiple myeloma but has recovered from its toxic effects. * measurable disease defined as 1 of the following: * serum M-protein ≥0.5 g/dL * urine M-protein ≥200 mg/24 hours * a life expectancy of more than 3 months. * an ECOG performance status of 0, 1, or 2. * adequate hepatic organ function. * an absolute neutrophil count (ANC), hemoglobin level, and platelet count within protocol-specific ranges. * been independent of granulocyte-colony stimulating factor (G-CSF) or granulocyte macrophage-colony stimulating factor (GM-CSF) support for more than 1 week. * been independent of platelet transfusion for more than 1 week. * received, or may have received, an allogeneic and/or autologous transplant. * a creatinine clearance of 30 mL/minute or more as measured or as calculated based on the Cockcroft-Gault method. * if the patient is a female of childbearing potential (not surgically sterile or 1 year postmenopausal): must use a medically accepted method of contraception (including abstinence) and must agree to continue use of this method for the duration of the study and for 3 months after participation in the study. * if the patient is a male: is surgically sterile, or if sexually active, is currently using an effective barrier method of contraception, and agrees to continue use of this method for the duration of the study and for 3 months after the last administration of study drug. Key Exclusion Criteria: The patient: * has nonmeasurable multiple myeloma. * received glucocorticoid therapy (prednisone \>10 mg/day orally or equivalent) within the last 2 weeks prior to the first dose of study drug. * has POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy or monoclonal proliferative disorder, and skin changes). * has plasma cell leukemia. * received chemotherapy with approved anticancer therapeutics within 2 weeks, or within 5 drug half-lives (t1/2), or investigative anticancer therapeutics within 4 weeks, or within 5 drug half-lives (t1/2), before the first dose of study drug, whichever time is greater. * received radiation therapy or immunotherapy in the 4 weeks prior to, or localized radiation therapy within 1 week prior to, the first dose of study drug. * received prior treatment with CEP-18770. * has used a medication known to be a potent inducer of CYP2E1, CYP2D6 or CYP3A4/5 within 4 weeks prior to the first dose of study drug. * has used a medication known to be a potent inhibitor of CYP2E1, CYP2D6 or CYP3A4/5 within 2 weeks prior to the first dose of study drug. * had major surgery within 3 weeks before the first dose of study drug. * has congestive heart failure or had symptomatic ischemia, conduction abnormalities uncontrolled by conventional intervention, or myocardial infarction within the last 6 months. * had an acute infection requiring systemic antibiotics, antiviral agents, or antifungal agents within 2 weeks before the first dose of study drug. * has a known or suspected human immunodeficiency virus (HIV) infection on the basis of medical history. * had a nonhematologic malignancy within the past 3 years except for the following: adequately treated basal cell or squamous cell skin cancer, carcinoma in situ of the cervix or breast, or prostate cancer (Gleason grade \<6 with prostate specific antigen (PSA) levels within the normal range). * has myelodysplastic or myeloproliferative syndrome. * has significant neuropathy. * is a pregnant or lactating woman. Any women becoming pregnant during the study will be withdrawn from the study. * has known central nervous system involvement. * has any serious psychiatric or medical condition that could interfere with treatment or study procedures, place the patient at unacceptable risk, or hinder the interpretation of study data. * has known hypersensitivity to mannitol or hydroxypropyl betadex.