Expanded Access Protocol Using Alpha/Beta T and CD19+ Depleted PBSC

PATIENT AND DONOR ELIGIBILITY Patients who lack an HLA matched sibling and who are candidates for allogeneic hematopoietic stem cell transplant (HSCT) but do not meet criteria for current open institutional protocols using CliniMACs device for β T/CD19+ depletion. Patients with matched related donors including matched sibling donors may also be eligible if special clinical indications are met. Patients with the following transplantable diseases: Non-malignant diseases: * Metabolic storage diseases correctable by HSCT * Bone marrow failure syndromes * Immunodeficiencies/immune dysregulation syndromes * Sickle cell disease or thalassemia * Other diseases treated with HSCT Malignant diseases: * Acute leukemias * Chronic leukemias * Lymphomas * Myelodyplastic syndrome Patient Eligibility criteria: It is important to note that the conditioning prescribed to the patient will be determined based on the disease and organ status and will include agents that are standard. Appropriate combinations of chemotherapy, immunotherapy and/or radiation will be determined on an individual basis. Patient eligibility will be assessed as per our institutional standard operating procedures: * Signed informed consent * Lansky or Karnofsky performance ≥ 60 * Hematologic and Organ Function as per current institutional SOP * Infectious Evaluation as per current institutional SOP * Participants of childbearing potential must have a negative pregnancy test as per institutional SOP * Subjects with graft failure who require a second HSCT will not need to meet eligibility criteria again prior to the second transplant. Graft failure is a medical emergency that requires HSCT Donor Eligibility Patients must have an identified living donor * Donor selection will comply with 21 CFR 1271\* * Unrelated donor that meets the matching criteria of the NMDP with allele matching at HLA -A, -B, -C, -DRB1, and -DQB1: Unrelated donors may be a 10/10 match, a 9/10 match, or an 8/10 match if one of the mismatches is at DQB1. * Related donor mismatched at one to five HLA alleles (haploidentical) * Matched related donor may be considered suitable donors for this protocol if a peripheral stem cell donation is deemed by the clinical team to be a safer donation option (if donor is not a suitable candidate for a bone marrow harvest) or if there is concern that bone marrow harvest would not yield adequate cell doses Additionally, a matched related donor would be considered suitable for this protocol if there are safety concerns regarding a patient receiving a standard T cell replete bone marrow transplant due to individualized GVHD risk or risk related to standard GVHD prevention medications. * Donor suitable for mobilization of peripheral stem cells and apheresis and fulfills infectious disease criteria as per our institutional SOP, including HIV, HepB, HepC PCR negative. * We assess donor eligibility as per our Allogenic Donor Evaluation for Eligibility standard operating procedure. These procedures apply for determining donor eligibility, including donor screening and testing for relevant communicable disease agents and diseases. Our donor collection program is FACT accredited. * Related donors will be consented and enrolled under IRB approved research protocol for cell collection per IRB 04-004078 CHP 784 Clinical and Research Collection and Future Research Use of Bone Marrow, Stem Cells or T Cells. * Unrelated donor identified through the National Marrow Donor Program (NMDP) and fulfills the NMDP criteria for donation. Unrelated donor willing and able to undergo mobilization of peripheral stem cells and apheresis. * The donors selected for this IDE will either be unrelated donors identified through the National Marrow Donor Program (NMDP) or related donors. Regarding the unrelated donors, NMDP procedures for determining donor eligibility include donor screening and testing for relevant communicable disease agents and diseases Exclusion criteria: * Uncontrolled bacterial, viral, or fungal infections * Fully HLA matched sibling donor (fully matched related donors including siblings may be included in special circumstances) * Donor unable to donate peripheral stem cells * Pregnant Females