Melphalan Hydrochloride in Treating Participants With Newly-Diagnosed Multiple Myeloma Undergoing Donor Stem Cell Transplantation

Inclusion Criteria: * Patients with non-relapsed multiple myeloma in complete response (CR), partial remission (PR), very good partial remission (VGPR), or symptomatic stable disease (no evidence of progression) including patients with light chain multiple myeloma (MM) detected in the serum by free light chain assay OR * Patients with non-secretory multiple myeloma (absence of a monoclonal protein \[M protein\] in serum as measured by electrophoresis \[serum protein electrophoresis (SPEP)\] and immunofixation (serum immunofixation electrophoresis \[SIFE\]) and the absence of Bence Jones protein in the urine \[urine protein electrophoresis (UPEP)\] defined by use of conventional electrophoresis and immunofixation \[urine immunofixation electrophoresis (UIFE) techniques\]) but with measurable disease on imaging studies like magnetic resonance imaging (MRI), computed tomography (CT) scan or positron emission tomography (PET) scan. * Patients who have received at least two cycles of initial systemic therapy and are within 2 to 12 months of the first dose. Mobilization therapy is not considered initial therapy. * Karnofsky performance score 70% or higher. * Left ventricular ejection fraction at rest \> 40% within 3 months of registration. * Bilirubin \< 2 x the upper limit of normal (except patients with Gilbert syndrome in whom bilirubin level of \> 2 x upper normal limit will be allowed) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \< 2.5 x the upper limit of normal. * Creatinine clearance of \>= 40 mL/min, estimated or calculated using the Cockcroft-Gault equation. * Pulmonary function: diffusing capacity of the lungs for carbon monoxide (DLCO), forced expiratory volume in one second (FEV1), forced vital capacity (FVC) \> 50% of predicted value (corrected for hemoglobin) within 3 months of registration. * All female and male subjects of reproductive potential must consent to the use of effective contraceptive methods as advised by the study doctor during treatment. * Signed informed consent form. Exclusion Criteria: * Patients with uncontrolled bacterial, viral or fungal infections (currently taking medication and progression of clinical symptoms). * Patients seropositive for the human immunodeficiency virus (HIV). * Patients with history of 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. * Patients participating in an investigational new drug protocol within 14 days before enrollment. * Female patients who are pregnant (positive beta-human chorionic gonadotropin \[b-HCG\]) or breast feeding. * Prior hematopoietic cell transplantation allogeneic or autologous (A prior autologous HCT will be allowed as long as it was part of tandem transplantation). * Prior organ transplant requiring immunosuppressive therapy