Inclusion Criteria:

1. Age ≥ 18 years and ≤ 70 years

2. Life expectancy ≥ 12 months

3. Eastern Cooperative Oncology Group (ECOG) performance status 0-2

4. Diagnosis of symptomatic multiple myeloma38, relapsed after initial therapy.

5. At least minimal response (defined as 25% decrease in the M protein in serum or
urine) to the most recent treatment regimen.

6. Evaluable disease prior to most recent treatment regimen as defined by at least one
of the following:

- Serum monoclonal (M) protein ≥0.5 g/dl by protein electrophoresis

- 200 mg of M protein in the urine on 24 hour electrophoresis

- Serum immunoglobulin free light chain ≥10 mg/dL AND abnormal serum
immunoglobulin kappa to lambda free light chain ratio

- Monoclonal bone marrow plasmacytosis ≥30%

7. 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 14 days prior to start of therapy

8. Hemoglobin ≥ 8 g/dL (80 g/L) within 14 days prior to start of therapy (subjects may
be receiving red blood cell [RBC] transfusions in accordance with institutional
guidelines)

9. Creatinine clearance (CrCl) ≥ 40 mL/minute within 14 days prior to start of therapy,
either measured or calculated using a standard formula (eg, Cockcroft and Gault).

10. Prior storage of at least 2 x 106 CD34+ cells/kg available for autologous
transplantation. During the phase 1 component of the study, at least the same amount
of cells is required as "back up" in the unlikely event of non-engraftment.

11. Subjects may have had a prior AHSCT for the treatment of MM as long as it was
performed greater than 12 months from study registration.

12. Subjects must meet institutional general eligibility criteria for autologous
transplantation.

13. Written informed consent in accordance with federal, local, and institutional
guidelines.

14. Female of childbearing potential (FCBP) must agree to ongoing pregnancy testing and
to practice contraception.

15. Male subjects must agree to practice contraception.

Exclusion Criteria:

1. Pregnant or lactating females.

2. Major surgery within 30 days prior to start of treatment.

3. Acute active infection requiring treatment (systemic antibiotics, antivirals, or
antifungals) within 14 days prior to randomization.

4. Known human immunodeficiency virus infection.

5. Active hepatitis B or C infection.

6. Unstable angina or 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.

7. Uncontrolled hypertension or uncontrolled diabetes within 14 days prior to
randomization.

8. Nonhematologic malignancy 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.

9. Significant neuropathy (Grades 3-4, or Grade 2 with pain) within 14 days prior to
randomization.

10. Known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize
carfilzomib).

11. Subjects with pleural effusions requiring thoracentesis or ascites requiring
paracentesis within 14 days prior to randomization.

12. 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.