Bone Marrow Transplantation Using CD34-Selected Stem Cells From Related or Unrelated Donors in Treating Participants With Cancer or Other Disorders

Inclusion Criteria: * Patients with malignant or nonmalignant diseases that can benefit from alternative stem cell transplantation according to institutional standard practice guidelines * Patients lacking a healthy human leukocyte antigen (HLA)-identical related donor and having one of the following alternative donor sources: * HLA-haploidentical related (HLA antigen genotypic match \>= 4/8 and \<= 7/8) or * Unrelated donor that is HLA matched at \>= 7/8 HLA antigen loci * The selected donor must also be: * Able to receive granulocyte colony-stimulating factor (G-CSF, filgrastim) and undergo apheresis either through placement of peripheral or temporary central venous catheter, based on institutional guidelines for peripheral blood stem cell collection * Meet all institutional standard criteria for clearance for peripheral stem cell collection * Recipients must meet institutional treatment standards based on pre-transplant evaluations including: * Adequate major organ functions * Free of major systemic infections * Not pregnant, if female of childbearing age (post-pubertal) * Recipient (if \>= 18 years) or their parent/legal guardian (if \< 18 years) must be able to sign the informed consent form for the treatment plan; assent will be obtained from recipients 7-17 years of age, in accordance to our institutional guidelines Exclusion Criteria: * Patients not meeting clearance criteria for bone marrow transplantation (BMT) based on standard institutional gui…