Autologous or Syngeneic Stem Cell Transplant Followed by Donor Stem Cell Transplant and Bortezomib in Treating Patients With Newly Diagnosed High-Risk, Relapsed, or Refractory Multiple Myeloma

Inclusion Criteria: * Newly diagnosed patients must have received induction therapy (e.g., vincristine, doxorubicin, dexamethasone \[VAD\], thalidomide/dexamethasone) for a minimum of 4 cycles * Must have the capacity to give informed consent * Must have an human leukocyte antigen (HLA) genotypically identical sibling or a phenotypically matched relative or, at a minimum, a high likelihood of identifying an HLA-matched unrelated donor; the determination of availability of a suitable unrelated donor may be based on a World-Book search * In addition, patients must meet at least one of the criteria A-I (A-G at time of diagnosis or pre-autograft): * A) Any abnormal karyotype by metaphase analysis except for isolated t(11,14) and constitutional cytogenetic abnormality * B) Fluorescence in situ hybridization (FISH) translocation 4;14 * C) FISH translocation 14;16 * D) FISH deletion 17p * E) Beta2-microglobulin \> 5.5 mg/L * F) Cytogenetic hypodiploidy * G) Plasmablastic morphology (\>= 2%) * DONOR: HLA genotypically identical sibling or phenotypically matched relative OR * DONOR: HLA phenotypically matched unrelated donor (according to Standard Practice HLA matching criteria, Grade #2.1) * Matched HLA-A, B, C, DRB1, and DQB1 alleles by high resolution typing. * Only a single allele disparity will be allowed for HLA-A, B, or C as defined by high resolution typing Exclusion Criteria: * Recurrent or non-responsive (less than partial response \[PR\]) MM after at least two different lines of conventional chemotherapy * Progressive MM after a previous autograft * Life expectancy severely limited by disease other than malignancy * Seropositive for the human immunodeficiency virus (HIV) * Females who are pregnant or breastfeeding * Fertile men or women unwilling to use contraceptive techniques during and for 12 months following treatment * Patients with active non-hematological malignancies (except non-melanoma skin cancers) or those with non-hematological malignancies (except non-melanoma skin cancers) who have been rendered with no evidence of disease, but have a greater than 20% chance of having disease recurrence within 5 years; this exclusion does not apply to patients with non-hematologic malignancies that do not require therapy * Patients with fungal infection and radiological progression after receipt of amphotericin B or active triazole for greater than 1 month * Patients with the following organ dysfunction: * Symptomatic coronary artery disease or ejection fraction \< 40% or other cardiac failure requiring therapy; 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 * Ejection fraction is required if the patient has a history of anthracyclines or history of cardiac disease * Diffusing lung capacity for carbon monoxide (DLCO) \< 50%, forced expiratory volume in 1 second (FEV) \< 50% and/or receiving supplementary continuous oxygen; the Fred Hutchinson Cancer Research Center (FHCRC) principle investigator (PI) of the study must approve of enrollment of all patients with pulmonary nodules * Liver function abnormalities: Patient with clinical or laboratory evidence of liver disease will be evaluated for the cause of liver disease, its clinical severity in terms of liver function, bridging fibrosis, and the degree of portal hypertension; the patient will be excluded if he/she is found to have fulminant liver failure; cirrhosis of the liver with evidence of portal hypertension; alcoholic hepatitis; esophageal varices; a history of bleeding esophageal varices; hepatic encephalopathy; uncorrectable hepatic synthetic dysfunction evinced by prolongation of the prothrombin time ascites related to portal hypertension; bacterial or fungal liver abscess; biliary obstruction; chronic viral hepatitis with total serum bilirubin \> 3 mg/dL; and symptomatic biliary disease; * Karnofsky score \< 70% for adult patients * Patient with poorly controlled hypertension and on multiple antihypertensives * Patients with current \>= grade 2 peripheral neuropathy * Patient has an active bacterial or fungal infection unresponsive to medical therapy * DONOR: Identical twin * DONOR: Donors unwilling to donate PBSC * DONOR: Pregnancy * DONOR: Infection with HIV * DONOR: Inability to achieve adequate venous access * DONOR: Known allergy to G-CSF * DONOR: Current serious systemic illness * DONOR: Failure to meet FHCRC criteria for stem cell donation * DONOR: Age \< 12 years * DONOR: A positive anti-donor cytotoxic crossmatch * DONOR: Patient and donor pairs must not be homozygous at mismatched allele