The purpose of the CliniMACS® TCRαβ-Biotin System and CliniMACS® CD19 is to improve the safety and efficacy of allogeneic HLA-partially matched related or unrelated donors HSCT when no matched donors are available, to treat malignant and nonmalignant disorders for which HSCT is the recommended best available therapy. Initially this device will be used in a single-center, open-label, single-arm, phase II clinical trial to evaluate the efficacy of haploidentical PBSC grafts depleted of TCRα/β+ and CD19+ cells using the CliniMACS® TCRαβ/CD19 System in children and adults with hematological and non-hematological malignancies.

Inclusion Criteria for Cohort M and Cohort NM:

1. Age < 60 years and > 1 month;

2. Life expectancy > 10 weeks;

3. Patients deemed eligible for allogeneic HSCT per institutional guidelines;

4. Patients with life-threatening hematological malignancies and non-malignant disorders that could benefit from HSCT;

   a. For malignant patients: i. High-risk acute lymphoblastic leukemia (ALL) in 1st complete remission (CR), ALL in 2nd CR; or ii. High-risk acute myeloid leukemia (AML) in 1st CR, AML in 2nd CR; or iii. Childhood Myelodysplastic Syndrome (MDS) with low blasts (cMDS-LB) or Childhood MDS with increased blasts (cMDS-IB); or iv. Juvenile myelomonocytic leukemia (JMML); or v. Mixed-phenotype acute leukemia (MPAL); or vi. Non-Hodgkin lymphomas in 2nd CR; or vii. Other hematologic malignancies in 1st or 2nd CR eligible for stem cell transplantation per institutional standard b. Patients with non-malignant disorders receiving first HSCT: i. using mis-matched donors, due to the absence of suitable HLA identical sibling or HLA phenotypically identical relative; or ii. whose disease put them at increased risk of graft rejection or GvHD (e.g., Fanconi Anemia, STAT1 gain of function) and therefore can benefit from receiving alpha beta depleted HSCT using as a donor either an HLA identical sibling or an HLA phenotypically identical (10/10 matched) donor;

5. A minimum genotypic identical match of 5/10 is required;

6. The donor and recipient must be identical, as determined by high resolution typing, in at least one allele of each of the following genetic loci: HLA-A, HLA-B, HLA-C, HLA-DQB1 and HLA-DRB1;

7. Lansky/Karnofsky score > 50; the Karnofsky Scale will be used in subjects ≥ 16 years of age, and the Lansky Scale will be used for those < 16 years of age.

8. All subjects ≥ 18 years of age must be able to give informed consent or adults lacking capacity to consent must have a legally authorized representative (LAR) available to provide consent. For subjects <18 years old their legal authorized representative (LAR) (i.e. parent or guardian) must give informed consent. Pediatric subjects will be included in age appropriate discussion and written assent will be obtained for those > 7 years of age, when appropriate

9. Male and female subjects of childbearing potential must agree to use an effective means of birth control to avoid pregnancy throughout the transplant procedure, while on immunosuppression, and if the subject experiences any chronic GvHD.

Exclusion Criteria for Cohort M and Cohort NM:

1. Pregnant or lactating females;
2. Has received a prior allogenic HSCT;
3. Secondary MDS or AML or treatment related MDS or AML;
4. Dysfunction of liver (ALT/AST > 10 times upper normal value, or direct bilirubin > 3 times upper normal value),
5. Serum creatinine > 1.5 times ULN (for patients not on dialysis) or unmanageable dysfunction of renal function while undergoing dialysis (for patients on dialysis);
6. Severe cardiovascular disease (congestive heart failure or left ventricular ejection fraction < 30%);
7. Current active infectious disease (including positive HIV serology or viral RNA);
8. Serious concurrent uncontrolled medical disorders;
9. Lack of patient's/parents'/guardian's informed consent;
10. Any severe concurrent disease which, in the judgement of the PI, would place the patient at increased risk during participation in the study.