Inclusion Criteria:

1. Age 18 to 75 years, inclusive.
2. Subjects must have multiple myeloma which requires treatment for relapsed disease and are eligible for the planned autologous HSCT.
3. Subjects must have had one previous autologous HSCT, at least one year prior to the planned autologous HSCT in this study.
4. Eastern Cooperative Oncology Group (ECOG) Performance Status of 0-2.
5. Negative beta-human chorionic gonadotropin (β-HCG) pregnancy test in all women of child-bearing potential.
6. Subjects who are surgically sterile (ie, have undergone orchidectomy or hysterectomy); female subjects who have been postmenopausal for at least 12 consecutive months; or subjects who agree to remain abstinent or to practice double-barrier forms of birth control from trial screening through 30 days (for females) and 90 days (for males) from the last dose of the investigational medicinal product (IMP). If employing birth control, two of the following precautions must be used: vasectomy, tubal ligation, vaginal diaphragm, intrauterine device (IUD), birth control pill, birth control implant, condom, or sponge with spermicide.
7. Subjects in whom the minimum stem cell dose of 2.0 x 10\^6 cluster of differentiation 34 (CD34)+ cells/kg has been collected.
8. Ability to provide written informed consent prior to initiation of any study-related procedures, and ability, in the opinion of the Principal Investigator, to comply with all requirements of the study.

Exclusion Criteria:

1. Prior treatment history of allogeneic HSCT for any medical reason, not limited to myeloma treatment.
2. Prior treatment history of more than one autologous HSCT or high-dose chemotherapy with stem cell rescue for any medical reason, not limited to myeloma treatment.
3. Prior treatment with busulfan or gemtuzumab ozogamicin for any reason.
4. Presence of a t(4;14) or p53 gene deletion as determined by fluorescence in situ hybridization (FISH) during the screening process or documented t(4; 14) or p53 gene deletion obtained during a time of active disease by any method.
5. Systemic amyloidosis.
6. Known allergy to boron or any components of bortezomib.
7. Left ventricular ejection fraction (LVEF) < 45% as measured by either multi-gated acquisition scan (MUGA) or echocardiogram (ECHO) performed within 75 days prior to day of busulfan test dose. If cyclophosphamide was used for stem cell harvest, an ECHO or MUGA must be done prior to enrollment to confirm adequate cardiac function.
8. Uncontrolled arrhythmia or symptomatic cardiac disease at the time of screening.
9. Symptomatic pulmonary disease, based on Forced Expiratory Volume in 1 Second (FEV1), Forced Vital Capacity (FVC) or Diffusing Capacity of the Lung for Carbon Monoxide (DLCO) < 50% of predicted (corrected for hemoglobin) measured within 75 days prior to day of busulfan test dose.
10. Aspartate transaminase (AST)/alanine transaminase (ALT) ≥ 3 x the upper limit of normal (ULN),
11. History of elevated total serum bilirubin >2 mg/dL that had been caused by previous chemotherapy at any point, or total bilirubin > 2.0 mg/dL at the time of screening with the exception of Gilbert's disease.
12. Hepatic synthetic dysfunction evident International Normalized Ratio (INR) ≥ 2.0 at the time of screening.
13. Any previous history of fulminant liver failure, cirrhosis, alcoholic hepatitis, esophageal varices, hepatic encephalopathy, ascites related to portal hypertension, bacterial or fungal liver abscess, biliary obstruction, and symptomatic biliary disease.
14. Prior total body irradiation therapy or radiation therapy directly applied to the liver.
15. Known history of or current hepatitis B, hepatitis C, HIV, or uncontrolled active infection of any kind at the time of test dose. If serology antibody studies are positive, a quantitative polymerase chain reaction (PCR) must be completed to confirm lack of active infection.
16. Serum creatinine >2.0 mg/dL at the time of Screening.
17. ≥ Grade 1 neuropathy with pain, or > Grade 2 neuropathy without pain (subjects with neuropathy caused by a previous regimen that is recovered to ≤ Grade 2 and stable without pain may be included).
18. Women who are pregnant or lactating.
19. Current or history of drug and/or alcohol abuse.
20. Use of other investigational therapies within 30 days