Bortezomib Based Consolidation in Multiple Myeloma Patients Completing Stem Cell Transplant

Inclusion Criteria:

* Creatinine =\< 2 mg/dL
* Absolute neutrophil count (ANC) \>= 1000/mm\^3
* Platelet count \>= 75000/mm\^3
* Hemoglobin \>= 8.0 g/dL
* Total bilirubin =\< 1.5 x upper limit of normal (ULN)
* Treated myeloma: Prior induction therapy (any) and followed by autologous stem cell transplantation
* Measurable disease at initial diagnosis, pre-stem cell transplant (SCT) or post-SCT of multiple myeloma as defined by at least ONE of the following:

  * Serum monoclonal protein \>= 0.5 g/dL
  * \> 200 mg of monoclonal protein in the urine on 24 hour electrophoresis
  * Serum immunoglobulin free light chain \>= 5 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio
  * Monoclonal bone marrow plasmacytosis \>= 30% (evaluable disease)
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2
* \< 120 days post SCT with no evidence of relapse or progression prior to registration
* Provide voluntary informed written consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care
* Negative serum pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only
* Willing to return to enrolling institution for follow-up during the active monitoring phase of the study
* Ability to complete questionnaire(s) by themselves or with assistance
* Female patients who:

  * Are postmenopausal for at least 1 year before the screening visit, OR
  * Are surgically sterile, OR
  * If they are of childbearing potential, agree to practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent through 30 days after the last dose of study treatment, OR agree to completely abstain from heterosexual intercourse
* Male patients, even if surgically sterilized (ie, status postvasectomy), who:

  * Agree to practice effective barrier contraception during the entire study treatment period and through 30 days after the last dose of study treatment, OR
  * Agree to completely abstain from heterosexual intercourse

Exclusion Criteria:

* Other active malignancy =\< 3 years prior to registration; EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix; NOTE: If there is a history of prior malignancy, they must not be receiving other specific treatment for their cancer
* Other co-morbidity which would interfere with patient's ability to participate in trial, e.g. uncontrolled infection, uncompensated heart or lung disease
* Other concurrent chemotherapy, radiotherapy, or any ancillary therapy considered investigational; NOTE: Bisphosphonates are considered to be supportive care rather than therapy, and are thus allowed while on protocol treatment
* Known to be human immunodeficiency virus (HIV), hepatitis C virus (HCV) or hepatitis B virus positive (HBV+)
* Hypersensitivity to study drugs, boron or mannitol
* Patient refractory to bortezomib (defined as patients who progressed while on bortezomib or within 60 days of receiving bortezomib)
* Any serious medical or psychiatric condition that would prevent the subject from complying with the protocol treatment and procedures
* Grade \>= 2 peripheral neuropathy
* Myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities; prior to study entry, any electrocardiogram (ECG) abnormality at screening must be documented by the investigator as not medically relevant
* Participation in clinical trials with other investigational agents not included in this trial, within 14 days of the start of this trial and throughout the duration of this trial
* Radiation therapy within 3 weeks before randomization; enrollment of subjects who require concurrent radiotherapy (which must be localized in its field size) should be deferred until the radiotherapy is completed and 3 weeks have elapsed since the last date of therapy
* Female patients who are lactating or pregnant