A Study of Immune Suppression Treatment for People With Sickle Cell Disease or β-Thalassemia Who Are Going to Receive an Allogeneic Hematopoietic Cell Transplantation (HCT)

Inclusion Criteria:

* Age ≥ 2 and ≤ 50 years
* Suitable haploidentical donor.
* Performance score ≥ 70% by Karnofsky Performance Scale or 0 to 1 by ECOG (age \> 16 years), or Lansky Play-Performance Scale ≥ 70% (age ≤ 16 years).
* Adequate major organ system function as demonstrated by:

  * For patients ≥ 18 years of age:
  * eGFR ≥ 50 mL/min by Cockcroft-Gault formula Formula: ((140 - Age) x Weight (kg)) / (72 x Serum Creatinine (mg/dL) Female Adjustment: Multiply result by 0.85
  * For patients \< 18 years of age:
  * Serum creatinine clearance: glomerular filtration rate \[GFR\]) must be \>50 mL/min/1.73 m2 as calculated by the Schwartz formula
* Conjugated (direct) bilirubin less than 3x upper limit of normal.
* ALT or AST ≤ 3 times institutional upper limit of normal.
* Left ventricular ejection fraction ≥ 50%.
* Diffusing capacity for carbon monoxide (DLCO) ≥ 50% predicted, corrected for hemoglobin. For children \< 7 years of age who are unable to perform PFT, oxygen saturation \> 92% on room air by pulse oximetry.
* For SCD patients: HbSS, HbSC, HbS/β° with one or more of the following complications:

  * Acute chest syndrome: 2 or more episodes in the 2 years preceding enrollment
  * Vaso-occlusive episodes: 3 or more episodes in the 2 years preceding enrollment
  * Recurrent priapism: 2 or more episodes in the 2 years preceding enrollment
  * History of osteomyelitis or osteonecrosis
  * Cerebrovascular disease:
* Imaging evidence of prior overt or silent stroke
* History of a neurologic event resulting in focal neurologic deficits lasting \> 24 hours
* Abnormal transcranial Doppler: Timed average maximum mean velocity ≥ 200 cm/sec in terminal portion of the carotid or proximal portion of the middle cerebral artery or \> 185 cm/sec plus evidence of intracranial vasculopathy if imaging TCD is used

  * Pulmonary hypertension: Confirmed by right heart catheterization with mean pulmonary arterial pressure ≥ 25 mmHg or mean pulmonary vascular resistance \> 2 Wood units
  * Red blood cell alloimmunization (\> 3 alloantibodies)
* For thalassemia patients: Any genotype, with all of the following:

  * Onset of red blood cell transfusion dependence during the first 3 years of life
  * RBC transfusion history \> 225 mL/kg/year or \> 15 lifetime RBC transfusions
  * Pre-transfusion hemoglobin ≤ 7 g/dL
  * Hepatosplenomegaly
* Patient or the patient's legal representative, parent(s) or guardian should be able to provide written informed consent. Assent of a minor if participant's age is at least seven and less than eighteen years.
* For sexually active men and women of childbearing potential, must agree to use a form of contraception considered effective and medically acceptable by the Investigator.

Exclusion Criteria:

* Prior myeloablative allogeneic HCT.
* Overt stroke or CNS instrumentation (e.g. for Moyamoya disease) within 6 months of enrollment.
* Liver cirrhosis. Mild fibrosis will be permitted, i.e. fine reticulin or grade 1 of 4, with bridging fibrosis.
* Hepatic iron content ≥ 3 mg Fe/g liver dry weight, if applicable
* Active hepatitis B or C.
* Other uncontrolled infections.
* Other malignancy/cancer diagnosis unless in remission after definitive therapy for a minimum of 2 years. Exceptions: Ductal carcinoma in situ, basal cell carcinoma, cervical intraepithelial neoplasia.
* Positive pregnancy test in a woman with child-bearing potential, defined as not post-menopausal for 12 months or no previous surgical sterilization.
* Inability to comply with medical therapy or follow-up.
* Known history of allergic reactions to any constituents of the stem cell product, including a known history of allergic reactions to DMSO.