Exploratory Trial to Estimate Proportion of Patients With Tumor Cell Contaminated Leukapheresis Products With and Without Bortezomib With In-vivo Purging - Multiple Myeloma (MM)

Inclusion Criteria: * Subjects must meet all of the inclusion criteria to participate in this study. * Ability to understand, and the willingness to sign a written Informed Consent Form * Diagnosis of multiple myeloma undergoing planned autologous stem cell transplantation * Age ≥ 18 years * Karnofsky Performance Status (KPS) 70 or above, Eastern Cooperative Oncology Group (ECOG) 0, 1 or 2 * Adequate organ and marrow function as defined below: * leukocytes ≥ 3,000/micro Liter (mcL) * absolute neutrophil count ≥ 1,500/mcL * platelets ≥ 100,000/mcL * total bilirubin within normal institutional limits NOTE: For this study, subjects with bilirubin levels \> 1.5 Upper Limit of Normal (ULN) are excluded from enrollment in this study. * Aspartate Aminotransferase (AST) ( Serum Glutamic Oxaloacetic Transaminase \[SGOT\]) ≤ 2.5 X institutional upper limit of normal * Alanine Aminotransferase (ALT) (Serum Pyruvic Glutamic Transaminase \[SPGT\]) ≤ 2.5 X institutional upper limit of normal * creatinine within normal institutional limits * Women of child-bearing potential and men with partners of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 30 days following completion of therapy. Should a woman or partner become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician and the investigator immediately. * A woman of child-bearing potential is any female (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria: * Has not undergone a hysterectomy or bilateral oophorectomy; or * Has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months) Exclusion Criteria: * Subjects meeting any of the exclusion criteria at baseline will be excluded from study participation. * Current or anticipated use of other investigational agents. NOTE the following clarification for this study: Prohibited Concurrent Therapy: Participation in clinical trials with other investigational agents that are not included in this trial, within 14 days of the start of this trial until 2 weeks after participant has received the last dose of bortezomib for mobilization. * Hypersensitivity to bortezomib, boron or mannitol or Granulocyte colony-stimulating factor (G-CSF) * Subject has received \> 6 months of lenalidomide (Revlimid®) therapy prior to stem cell collection * Subject has known brain metastases. Presence of brain metastases should be excluded from this clinical trial because of poor prognosis and because patients often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * Grade 3 or higher peripheral neuropathy * Bilirubin levels \> 1.5 ULN * Uncontrolled inter-current illness including, but not limited to * ongoing or active infection * symptomatic congestive heart failure * unstable angina pectoris * cardiac arrhythmia * psychiatric illness/social situations that would limit compliance with study requirements * Pregnant or nursing: There is a potential for congenital abnormalities and for this regimen to harm nursing infants.