Bortezomib, Thalidomide, and Dexamethasone After Melphalan and Stem Cell Transplant in Treating Patients With Stage I-III Multiple Myeloma

Inclusion Criteria: * Multiple Myeloma patients with symptomatic disease, stage II or III at diagnosis or progressive stage I requiring chemotherapy and/or radiation therapy (by Salmon-Durie classification), who are not eligible for tandem transplant study using TMI; because of previous radiation or eligibility criteria; documentation of disease staging by both Salmon-Durie classification and International Staging System (ISS) is required * Patients with non-secretory myeloma should have measurable serum free-light chain protein by the Free-lite test or measurable disease such as a soft tissue myeloma * A minimum of 4 x 10\^6 of CD 34 Positive cell/kg has been harvested * A Karnofsky performance status (KPS) of \>= 70% is required unless the KPS is impaired due to bone disease * No contraindication to the collection of a minimum of 4 x 10\^6 CD34+ cells/kg by apheresis * All patients must have signed a voluntary, informed consent in accordance with institutional and federal guidelines * Bilirubin =\< 1.5 mg/dl * Serum glutamic oxaloacetic transaminase (SGOT) and serum glutamic pyruvate transaminase (SGPT) \< 2.5 x upper limits of normal * Creatinine clearance of \>= 40cc/min * Absolute neutrophil count of \> 1000/ul * Platelet count of \> 100,000/ul * Cardiac ejection fraction \>= 45% by multigated acquisition (MUGA) scan and/or by echocardiogram * Diffusing capacity of the lung for carbon monoxide (DLCO) \>= 50% of predicted lower limit * Human immunodeficiency virus (HIV) …