Inclusion Criteria:

1. Symptomatic multiple myeloma

2. Measurable disease, as defined by one or both of the following:

   • Serum M-protein ≥ 0.5 g/dL
   • Urine Bence-Jones protein ≥ 200 mg/24 hours
   • For IgA patients whose disease can only be reliably measured by serum quantitative immunoglobulin (qIgA) ≥ 750 mg/dL (0.75 g/dL)
3. Prior treatment with at least one, but no more than three, regimens for multiple myeloma
4. Documented relapse or progressive disease on or after any regimen
5. Achieved a response to at least one prior regimen
6. Age ≥ 18 years
7. Life expectancy ≥ 3 months
8. Eastern Cooperative Oncology Group performance status 0-2
9. Adequate hepatic function, with serum ALT ≤ 3.5 times the upper limit of normal and serum direct bilirubin ≤ 2 mg/dL (34 µmol/L) within 21 days prior to randomization
10. Absolute neutrophil count ≥ 1.0 × 109/L within 21 days prior to randomization
11. Hemoglobin ≥ 8 g/dL (80 g/L) within 21 days prior to randomization
12. Platelet count ≥ 50 × 109/L (≥ 30 × 109/L if myeloma involvement in the bone marrow is > 50%) within 21 days prior to randomization
13. Creatinine clearance (CrCl) ≥ 50 mL/minute within 21 days prior to randomization
14. Written informed consent in accordance with federal, local, and institutional guidelines
15. Females of childbearing potential must agree to ongoing pregnancy testing and to practice contraception
16. Male subjects must agree to practice contraception

Exclusion Criteria:

1. If previously treated with bortezomib (alone or in combination), progression during treatment

2. If previously treated with a lenalidomide and dexamethasone (len/dex) combination:

   • Progression during the first 3 months of initiating treatment
   • Any progression during treatment if the len/dex regimen was the subject's most recent line of therapy
3. Discontinuation of previous lenalidomide or dexamethasone due to intolerance; subjects who are intolerant to bortezomib are not excluded
4. Prior carfilzomib treatment
5. POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes)
6. Waldenström's macroglobulinemia or IgM myeloma
7. Plasma cell leukemia (> 2.0 × 10^9/L circulating plasma cells by standard differential)
8. Chemotherapy or investigational agent within 3 weeks prior to randomization or antibody therapy within 6 weeks prior to randomization
9. Radiotherapy to multiple sites or immunotherapy/antibody therapy within 28 days prior to randomization; localized radiotherapy to a single site within 7 days prior to randomization
10. Corticosteroid therapy at dose equivalent to dexamethasone > 4 mg/day within 21 days prior to randomization
11. Pregnant or lactating females
12. Major surgery within 21 days prior to randomization
13. Acute active infection requiring treatment (systemic antibiotics, antivirals, or antifungals) within 14 days prior to randomization
14. Known human immunodeficiency virus infection
15. Active hepatitis B or C infection
16. Myocardial infarction within 4 months prior to randomization, NYHA Class III or IV heart failure, uncontrolled angina, history of severe coronary artery disease, severe uncontrolled ventricular arrhythmias, sick sinus syndrome, or electrocardiographic evidence of acute ischemia or Grade 3 conduction system abnormalities unless subject has a pacemaker
17. Uncontrolled hypertension or uncontrolled diabetes within 14 days prior to randomization
18. Other malignancy, including MDS, within the past 3 years with the exception of a) adequately treated basal cell carcinoma, squamous cell skin cancer, or thyroid cancer; b) carcinoma in situ of the cervix or breast; c) prostate cancer of Gleason Grade 6 or less with stable prostate-specific antigen levels; or d) cancer considered cured by surgical resection or unlikely to impact survival during the duration of the study, such as localized transitional cell carcinoma of the bladder or benign tumors of the adrenal or pancreas
19. Significant neuropathy (Grades 3-4, or Grade 2 with pain) within 14 days prior to randomization
20. Known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib)
21. Contraindication to any of the required concomitant drugs or supportive treatments, including hypersensitivity to all anticoagulation and antiplatelet options, antiviral drugs, or intolerance to hydration due to preexisting pulmonary or cardiac impairment
22. Ongoing graft-vs-host disease
23. Subjects with pleural effusions requiring thoracentesis or ascites requiring paracentesis within 14 days prior to randomization
24. Any other clinically significant medical disease or condition that, in the Investigator's opinion, may interfere with protocol adherence or a subject's ability to give informed consent