Radioimmunotherapy (211At-OKT10-B10) and Chemotherapy (Melphalan) Before Stem Cell Transplantation for the Treatment of Multiple Myeloma

Inclusion Criteria: * Patients with a diagnosis of multiple myeloma * Patients must have autologous hematopoietic stem cells collected with a minimum CD34+ stem cell yield of \>= 4 x 10\^6 CD34+ cells/kg of body weight * Subjects must have disease meeting criteria for clinical relapse or progressive disease (International Myeloma Working Group \[IMWG\] consensus criteria) and a history of \>= 1 prior autologous stem cell transplant(s) * Subjects must have received at least 3 prior lines of therapy: an immunomodulatory drug, a proteasome inhibitor, and a CD38-targeting antibody \* Aline of therapy is defined as one or more cycles of a planned treatment program. This may consist of one or more planned cycles of a single-agent therapy or combination therapy, as well as a sequence of treatments administered in a planned manner. For example, a planned treatment approach of induction therapy followed by autologous stem cell transplantation, followed by maintenance is considered one line of therapy. A new line of therapy starts when a planned course of therapy is modified to include other treatment agents (alone or in combination) as a results of disease progression, relapse, or toxicity. A new line of therapy also starts when a planned period of observation off therapy is interrupted by a need for additional treatment for the disease * Subjects must have an estimated creatinine clearance greater than 60 ml per minute by the following formula (Cockcroft-Gault). Serum creatinine value must be within 28 +/- days prior to registration * Subjects must have an Eastern Cooperative Oncology Group (ECOG) score =\< 2 or Karnofsky score \>= 70% * Ability to provide informed consent * Subjects 18 years of age Exclusion Criteria: * Subjects with a history of plasma cell leukemia * History of central nervous system involvement by multiple myeloma * Prior radioimmunotherapy or radiation of \> 20 Gy to pelvis or at maximally tolerated levels to any critical normal organ * Prior allogeneic hematopoietic cell transplant * More than 2 prior autologous hematopoietic cell transplants * Subjects with medullary or extramedullary plasmacytoma/s measuring \> 3 cm by magnetic resonance imaging (MRI) or positron emission tomography (PET)-computed tomography (CT) (radiated lesions are exempt from this criterion) * Subjects with a history of any one of the following cardiovascular conditions within the past 6 months: Class III or IV heart failure as defined by the New York Heart Association (NYHA), cardiac angioplasty or stenting, myocardial infarction, unstable angina, or other clinically significant cardiac disease as determined by the principal investigator (PI) or designee * Subjects with corrected QT (QTc) prolongation at baseline * Subjects with a history of cardiac arrhythmia and a heart rate \> 100 beats per minute (BPM) (oral beta-blocker \[excluding sotalol\] and/or calcium channel blocker therapy are acceptable to achieve rate control) * History of reactive airway disease and clinically significant asthma requiring any form of medical treatment in the prior three months * Left ventricular ejection fraction \< 40% * Corrected diffusing capacity of the lungs for carbon monoxide (DLCO) \< 50% or receiving supplemental continuous oxygen * Liver abnormalities: fulminant liver failure, cirrhosis of the liver with evidence of portal hypertension, alcoholic hepatitis, esophageal varices, hepatic encephalopathy, uncorrectable hepatic synthetic dysfunction as evidenced by prolongation of the prothrombin time, ascites related to portal hypertension, bacterial or fungal liver abscess, biliary obstruction, chronic viral hepatitis, or symptomatic biliary disease. * Bilirubin \> 2 times the upper limit of normal * Aspartate aminotransferase \[AST\] and alanine aminotransferase \[ALT\] \> 2 times the upper limit of normal * Subjects who are known to be seropositive for human immunodeficiency virus (HIV) * Women of childbearing potential who are pregnant (beta-human chorionic gonadotropin \[HCG\]+) or breast feeding * Fertile subjects unwilling to use contraceptives during and for 12 months post-transplant * Subjects with untreated and uncontrolled infection at time of enrollment * Subjects with known amyloid light-chain (AL) subtype amyloidosis * Known allergy to murine-based monoclonal antibodies * Known contraindications to radiotherapy * History of another primary malignancy that has not been in remission for at least 2 years (the following are exempt from the 2-year limit: non-melanoma skin cancer, curatively treated localized prostate cancer, and cervical carcinoma in situ on biopsy or a squamous intraepithelial lesion on Papanicolaou \[PAP\] smear) * Any anti-CD38 monoclonal antibody within 30 days of anticipated date of infusion of 211At-OKT10-B10 * Individuals with a history of CTCAE grade 4 gastrointestinal toxicity associated with prior high-dose melphalan conditioning therapy (previous autologous stem cell transplant)