Busulfan, Melphalan, and Bortezomib Before First-Line Stem Cell Transplant in Treating Patients With Multiple Myeloma

Inclusion Criteria: * Patients must have histologically or cytologically confirmed multiple myeloma * Measurable disease must be present as defined by protein criteria (quantifiable M-component in serum, urine or serum free light chains) in order to evaluate response as per IMWG; non-secretory patients are eligible provided the patient has \> 20% plasmacytosis OR multiple (\> 3) focal plasmacytomas or focal lesions on magnetic resonance imaging (MRI) * Patients must have received induction chemotherapy for myeloma, but not more than 12 months of prior chemotherapy for this disease, and must be eligible for the first planned autologous transplant * A minimum stem cell dose of 2.0 x 10\^6 cluster of differentiation 34-positive (CD34+) cells/kg has been collected * Life expectancy of greater than 12 months * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/mcL (unless myeloma related) * Absolute neutrophil count \>= 1,500/mcL (unless myeloma related) * Platelets \>= 50,000/mcL (unless myeloma related) * Total bilirubin =\< 2 x institutional upper limit of normal unless 2nd to Gilbert's disease * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional upper limit of normal * Creatinine =\< 1.5 x institutional upper limit of normal OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Ejection fraction by echocardiogram (ECHO) or multi gated acquisition scan (MUGA) \>= 40% performed within 60 days prior to registration * Patients must have adequate pulmonary function studies: \> 50% of predicted on mechanical aspects (forced expiratory volume in one second \[FEV1\], forced vital capacity \[FVC\]) and diffusion capacity (diffusing capacity of the lung for carbon monoxide \[DLCO\]) \> 50% of predicted, within 60 days of registration; if the patients is unable to complete pulmonary function tests due to multiple myeloma (MM) related pain or condition, exception may be granted if the principal investigator (PI) documents that the patient is a candidate for high dose therapy * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for at least six months following the stem cell transplantation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Prior treatment history of autologous hematopoietic stem cell transplant (HSCT) or high-dose chemotherapy with stem cell rescue for any medical reason, not limited to myeloma treatment * Patients may not be receiving any other investigational agents * Patients with known brain metastases should be excluded from this clinical trial * History of allergic reactions attributed to compounds of similar chemical or biologic composition to or other agents used in the study, such as busulfan, melphalan, bortezomib, boron, or mannitol * Grade 2 or greater peripheral neuropathy within 14 days prior to enrollment * Unresolved grade \>= 3 non-hematologic toxicity from previous therapy; patients with grade 2 toxicity will be eligible at the discretion of the PI * Prior malignancies except resected basal cell carcinoma or treated cervical carcinoma in situ; cancer treated with curative intent \< 5 years will not be allowed unless approved by the PI; cancer treated with curative intent \> 5 years will be allowed * Patients must not have significant co-morbid medical condition * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements; patients must not have suffered recent (\< 6 months) myocardial infarction, unstable angina, difficult to control congestive heart failure, uncontrolled hypertension, or difficult to control cardiac arrhythmias * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with busulfan * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Patients found to have an active hepatitis B infection (hepatitis B surface antigen +) are not eligible unless they meet ONE of the following criteria: * Patient is able to start dual anti-hepatitis (Hep) B therapy prior to enrollment with adefovir and telbivudine * Patient is already on dual anti-hepatitis B therapy * Consultation and co-management with a hepatitis expert regarding hepatitis B treatment is strongly encouraged before and during the trial * Patients, who are positive for hepatitis B core antibody, but negative for the hepatitis B surface antigen, should be started on lamivudine 100 mg daily until at least 3 months post stem cell transplant