Inclusion Criteria:

1. Multiple myeloma with relapsing or progressing disease at study entry.
2. Patients must have evaluable multiple myeloma with, at least one of the following (assessed within 21 days prior to randomization):
   • Serum M-protein ≥ 0.5 g/dL, or
   • Urine M-protein ≥ 200 mg/24 hour, or
   • In patients without detectable serum or urine M-protein, serum free light chain (SFLC) > 100 mg/L (involved light chain) and an abnormal kappa/lamda ratio (>4:1 or <2:1), or
   • For IgA patients whose disease can only be reliably measured by serum quantitative immunoglobulin (qIgA) ≥ 750 mg/dL (0.75 g/dL).
3. Patients must have documented at least PR to at least 1 line of prior therapy. PR documentation can be based on Investigator assessment.
4. Received 1, but no more than 3 prior treatment regimens or lines of therapy for multiple myeloma. (Induction therapy followed by stem cell transplant and consolidation/maintenance therapy will be considered as one line of therapy).
5. Prior therapy with Velcade is allowed as long as the patient had at least a PR to prior Velcade therapy, was not removed from Velcade therapy due to toxicity, and will have at least a 6 month Velcade treatment-free interval from last dose received until first study treatment. (Patients may receive maintenance therapy with drugs that are not in the proteasome inhibitor class during this 6 month Velcade treatment-free interval).
6. Prior therapy with carfilzomib is allowed as long as the patient had at least a PR to prior carfilzomib therapy, was not removed from carfilzomib therapy due to toxicity, and had at least a 6-month carfilzomib treatment-free interval from last dose received until first study treatment. (Patients may receive maintenance therapy with drugs that are not in the proteasome inhibitor class during this 6 month carfilzomib treatment-free interval). The exception to this is patients randomized or previously randomized in any other Onyx-Sponsored Phase 3 trial.
7. Males and females ≥ 18 years of age.
8. Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 to 2.
9. Adequate hepatic function within 21 days prior to randomization, with bilirubin < 1.5 times the upper limit of normal (ULN), and aspartate aminotransferase (AST) and alanine aminotransferase (ALT) < 3 times the ULN.
10. LVEF ≥ 40%. 2-D transthoracic echocardiogram (ECHO) is the preferred method of evaluation. Multigated Acquisition Scan (MUGA) is acceptable if ECHO is not available.
11. Absolute neutrophil count (ANC) ≥ 1000/mm3 within 21 days prior to randomization. Screening ANC should be independent of growth factor support for ≥ 1 week.
12. Hemoglobin ≥ 8.0 g/dL within 21 days prior to randomization. Use of erythropoietic stimulating factors and red blood cell (RBC) transfusions per institutional guidelines is allowed, however most recent RBC transfusion may not have been done within 7 days prior to obtaining screening hemoglobin.
13. Platelet count ≥ 50,000/mm3 (≥ 30,000/mm3 if myeloma involvement in the bone marrow is > 50%) within 21 days prior to randomization. Patients should not have received platelet transfusions for at least 1 week prior to obtaining the screening platelet count.
14. Calculated or measured creatinine clearance (CrCl) of ≥ 15 mL/min within 21 days prior to randomization. Calculation should be based on standard formula such as the Cockcroft and Gault:

    [(140 - Age) x Mass (kg) / (72 x Creatinine mg/dL)]; multiply result by 0.85 if female.

15. Written informed consent in accordance with federal, local, and institutional guidelines.
16. Female patients of child-bearing potential (FCBP) must have a negative serum pregnancy test within 21 days prior to randomization and agree to use an effective method of contraception during and for 3 months following last dose of drug (more frequent pregnancy tests may be conducted if required per local regulations). Postmenopausal females (> 45 years old and without menses for > 1 year) and surgically sterilized females are exempt from a pregnancy test.
17. Male patients must use an effective barrier method of contraception during study and for 3 months following the last dose if sexually active with a female of child-bearing potential.

Exclusion Criteria:

1. Multiple Myeloma of IgM subtype.
2. Glucocorticoid therapy (prednisone > 30 mg/day or equivalent) within 14 days prior to randomization.
3. POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes).
4. Plasma cell leukemia or circulating plasma cells ≥ 2 × 109/L.
5. Waldenstrom's Macroglobulinemia.
6. Patients with known amyloidosis.
7. Chemotherapy with approved or investigational anticancer therapeutics within 21 days prior to randomization.
8. Patients randomized or previously randomized in any other Onyx-Sponsored Phase 3 trial.
9. Focal radiation therapy within 7 days prior to randomization. Radiation therapy to an extended field involving a significant volume of bone marrow within 21 days prior to randomization (i.e., prior radiation must have been to less than 30% of the bone marrow).
10. Immunotherapy within 21 days prior to randomization.
11. Major surgery (excluding kyphoplasty) within 28 days prior to randomization.
12. Active congestive heart failure (New York Heart Association [NYHA] Class III to IV), symptomatic ischemia, or conduction abnormalities uncontrolled by conventional intervention. Myocardial infarction within four months prior to randomization.
13. Acute active infection requiring systemic antibiotics, antiviral (except antiviral therapy directed at hepatitis B) or antifungal agents within 14 days prior to randomization.
14. Known HIV seropositive, hepatitis C infection, and/or hepatitis B (except for patients with hepatitis B surface antigen [SAg] or core antibody receiving and responding to antiviral therapy directed at hepatitis B: these patients are allowed).
15. Patients with known cirrhosis.
16. Second malignancy within the past 3 years except:
    • adequately treated basal cell or squamous cell skin cancer
    • carcinoma in situ of the cervix
    • prostate cancer < Gleason score 6 with stable prostate-specific antigen (PSA) over 12 months
    • breast carcinoma in situ with full surgical resection
    • treated medullary or papillary thyroid cancer
17. Patients with myelodysplastic syndrome.
18. Significant neuropathy (Grades 3 to 4, or Grade 2 with pain) within 14 days prior to randomization.
19. Female patients who are pregnant or lactating.
20. Known history of allergy to Captisol(a cyclodextrin derivative used to solubilize carfilzomib).
21. Patients with hypersensitivity to carfilzomib, Velcade, boron, or mannitol.
22. Patients with contraindication to dexamethasone.
23. Contraindication to any of the required concomitant drugs or supportive treatments, including hypersensitivity to antiviral drugs, or intolerance to hydration due to preexisting pulmonary or cardiac impairment.
24. Ongoing graft-vs-host disease.
25. Patients with pleural effusions requiring thoracentesis or ascites requiring paracentesis within 14 days prior to randomization.