Inclusion Criteria:

* Ability to understand and sign informed consent
* Age ≥ 18 years and ≤ 65 years
* Patients should be in very good partial response (VGPR) (5% or less plasma cells in the marrow) or better response status at the time of stem cell transplant with no evidence of central nervous system (CNS) disease. Patients in complete response (CR) should have minimal residual disease (MRD) positivity
* Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 1; or Karnofsky performance status (KPS) of ≥ 70%
* ≥ 60 days washout period from the last dose of an anti-CD38 antibody before the allogeneic transplant
* ≥ 6 months washout period from the last autologous transplant before the allogeneic transplant
* Related or unrelated donors available as follows:

* Sibling donor who is a 7/8 mismatched or 8/8 matched for human leukocyte antigen (HLA)-A, -B, -C, -DRB1
* Matched unrelated donor who is a 7/8 mismatched or 8/8 matched for HLA-A, -B, -C, and -DRB1
* A diagnosis of relapsed or refractory defined as:

* Primary refractory disease or relapse \< 12 months following initial therapy that includes an immunomodulatory agent, proteasome inhibitor, anti-CD38 monoclonal antibody, and corticosteroid
* Relapse \< 12 months after first autologous stem cell transplant
* Failing to achieve complete response or relapsing after chimeric antigen receptor (CAR)-T treatment or bispecific antibodies; or indicated but ineligible for either bispecific antibodies or CAR-T cells due to low blood counts
* No appropriate standard of care therapy per investigator
* A diagnosis of ultra-high risk multiple myeloma defined as having at least one or more of these criteria:

* Biallelic TP53 inactivation
* ≥ 2 HRCAs: del(17p), TP53 mutation, t(4;14), t(14;16), t(14;20), gain(1q), amp(1q), del(1p32)
* Biallelic del(1p32)
* High-risk gene expression profile signature
* Extramedullary disease excluding intramedullary plasmacytoma with extraosseous extension and active CNS disease
* ≥ 2% circulating plasma cells
* Creatinine clearance of ≥ 50 mL/min as estimated by Cockcroft-Gault
* Total bilirubin ≤ 1.5 times upper limit of normal (ULN) except in subjects with Gilbert's syndrome in whom total bilirubin ≤ 3 times ULN
* Alanine transaminase (ALT/serum glutamic pyruvic transaminase \[SGPT\]) and aspartate aminotransferase (AST/serum glutamic oxaloacetic transaminase \[SGOT\]) ≤ 3 x the upper limit of normal (ULN) or ≤ 5 x ULN if documented liver involvement by disease
* Estimated glomerular filtration rate (eGFR) \> 50mL/minute. Creatinine clearance of ≥ 30 mL/min is allowed in patients eligible for no tacrolimus immunosuppression
* Pulmonary function as defined by diffusing capacity of the lung for carbon monoxide (DLCO) (adjusted for hemoglobin) ≥ 50%
* Cardiac ejection fraction at rest ≥ 45% or shortening fraction of ≥ 27% by echocardiogram, or radionuclide scan (multigated acquisition scan \[MUGA\])
* Corrected diffusing capacity of the lung for carbon monoxide (DLCO) (adjusted for hemoglobin) ≥ 50%
* Individuals of childbearing potential or those with partners of childbearing potential must agree to use methods of contraception for the duration of study participation or be surgically sterilized
* Stated ability and willingness to adhere to the study visit schedule and protocol requirements
* DONOR: Ability to understand and sign informed consent
* DONOR: Age ≥ 16 and ≤ 35 years at time of enrollment for unrelated donors and Age ≥ 16 and ≤ 50 years for related donors
* DONOR: Either one of the following scenarios:

* Sibling donor who is a 7/8 mismatched or 8/8 matched for HLA-A, -B, -C, and -DRB1, all typed using deoxyribonucleic acid (DNA)-based high-resolution methods
* Unrelated donor who is 7/8 mismatched or 8/8 matched HLA-A, -B, -C, and -DRB1, all typed using DNA-based high-resolution methods
* DONOR: Willing to donate stem cell mobilized mononuclear cells for up to two consecutive days
* DONOR: Able to donate within the continental United States at a site that will employ a Spectra Optia Apheresis System for post-mobilization apheresis
* DONOR: Meets federal eligibility criteria for donors of viable, leukocyte-rich cells or tissues and all relevant Food and Drug Administration (FDA) Guidance for Industry (Eligibility Determination for Donors of Human Cells, Tissues, and Cellular and Tissue-Based Products, 2007; Use of Donor Screening Tests to Test Donors of Human Cells, Tissues and Cellular and Tissue-Based Products for Infection with Treponema pallidum \[syphilis\], 2015; Use of Nucleic Acid Tests to Reduce the Risk of Transmission of Hepatitis B Virus from Donors of Human Cells, Tissues, and Cellular and Tissue-Based Products, 2016; Use of Nucleic Acid Tests to Reduce the Risk of Transmission of West Nile Virus from Living Donors of Human Cells, Tissues, and Cellular and Tissue-Based Products \[HCT/Ps\], 2016)
* DONOR: Donors determined to be ineligible, based on the results of required testing and/or screening, may nonetheless be included if either applies:

* The donor is a first-degree blood relative of the recipient
* Urgent medical need, meaning no comparable human cell product is available, and the recipient is likely to suffer death or serious morbidity without the human cell product, as attested by the investigator
* Meets any other criteria for donation as specified by standard National Marrow Donor Program (NMDP) guidelines (NMDP donors) or institutional standards (non-NMDP donors)

Exclusion Criteria:

* Prior allogeneic hematopoietic cell transplantation (HCT)
* Planned pharmaceutical in vivo or ex vivo T cell depletion, e.g., post-transplant cyclophosphamide (Cy), peri-transplant anti-thymocyte globulin (ATG), or alemtuzumab
* Positive anti-donor HLA antibodies against a mismatched allele in the selected donor determined by either:

* A positive crossmatch test of any titer; or
* The presence of anti-donor HLA antibody to any HLA locus
* Hematopoietic cell transplantation-specific Comorbidity Index (HCT-CI) \> 4
* Uncontrolled bacterial, viral, or fungal infections (currently taking antimicrobial therapy and with no clinical improvement) at time of enrollment
* Seropositive for HIV-1 or -2, human T-cell lymphotropic virus (HTLV)-1 or -2
* Documented allergy or documented hypersensitivity to iron dextran or bovine, murine, algal or Streptomyces avidinii proteins
* Concurrent malignancies or active disease within 1 year, except non-melanoma skin cancers or any carcinoma in situ that have been curatively resected
* History of idiopathic or secondary myelofibrosis
* Individuals who are pregnant or breastfeeding
* Any condition that would prohibit the understanding or rendering of informed consent
* Any condition that in the opinion of the investigator would interfere with the subject's safety or compliance while on study
* A diagnosis of polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy, and skin changes (POEMS) syndrome
* DONOR: Evidence of uncontrolled, active infection
* DONOR: Seropositive for HIV-1 or -2, HTLV-1 or -2
* DONOR: Positive for hepatitis B (HBV) surface antigen (HBsAg), total anti-hepatitis B core antibody (HBcAb, immunoglobulin \[I\]gG and IgM), HBV nucleic acid testing (NAT), anti-hepatitis C (HCV) antibody, or HCV NAT
* DONOR: Aberrant CD45RA isoform expression
* DONOR: Women who are pregnant or breastfeeding