NMA Haplo or MUD BMT for Newly Diagnosed Severe Aplastic Anemia

Inclusion Criteria: * Confirmed diagnosis of inherited or acquired severe aplastic anemia (SAA) * One of the following available donors: 1. HLA-haploidentical relative 2. If recipient is \>= 40 years old, may use HLA-matched related donor 3. For recipients with inherited bone marrow failure syndromes (IBMFS) with clear evidence of same disorder in potential related donors, may use 10/10 matched unrelated donor * Recipient and/or legal guardian must sign protocol informed consent * Donor must be willing to donate bone marrow * Left ventricular ejection fraction (LVEF) \>= 40%. For recipients \< 13 years old, shortening fraction \>= 26% may be used instead. * Bilirubin \< 3 x upper limit of normal (ULN) for age, unless patient has Gilbert's disease * aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 5 x ULN for age * For patients \>= 13 years old: estimated creatinine clearance \> 50 mL/min using Cockcroft-Gault formula and actual body weight * For patients \>= 1 but \< 13 years old: glomerular filtration rate (GFR) estimated by updated Schwartz formula \>= 90 mL/min/1.73 m\^2. If estimated GFR is \< 90 mL/min/1.73 m\^2, 24-hour measured creatinine clearance must be \> 50 mL/min/1.73 m\^2. * For patients \>= 8 years old, diffusing capacity of the lung for carbon monoxide (DLCO) (corrected for hemoglobin) \> 40%; forced expiratory volume at one second (FEV1) \> 50%; forced vital capacity (FVC) \> 50% * For patients \< 8 years old or unable to undergo pulmonary function testing: no evidence of dyspnea at rest; no need for supplemental oxygen; oxygen saturation \> 92% on room air * Karnofsky/Lansky status (depending on age) \>= 70% * Females and males of childbearing potential must agree to practice 2 effective methods of contraception at the same time. If unwilling, they must agree to complete abstinence. Exclusion Criteria: * Previous administration of immunosuppressive therapy for SAA. * Fanconi anemia. At minimum, this diagnosis must be excluded by diepoxybutane (DEB) or equivalent testing on peripheral blood or marrow in patients \< 30 years old. * Clonal cytogenetic abnormalities consistent with pre-myelodysplastic syndrome (pre-MDS) or MDS on bone marrow examination * Presence of anti-donor antibodies * Prior allogeneic stem cell transplant * Prior solid organ transplant * Uncontrolled bacterial, viral, or fungal infection * HIV seropositivity * Active hepatitis B or C infection determined by serology and/or nucleic acid testing (NAT) * Pregnancy or active breastfeeding * Prior malignancies except: resected basal carcinoma or treated cervical carcinoma in situ; cancer treated with curative intent \> 5 years previously. Other prior cancers will not be allowed unless approved by the PI.