Has undergone allo-HSCT from any donor (related or unrelated with any degree of HLA matching) and any donor source (bone marrow, peripheral blood stem cells, or cord blood) for a hematologic malignancy or disorder. Recipients of myeloablative and reduced-intensity conditioning regimens are eligible. DONOR: Only filgrastim (G-CSF) mobilized PBSC only will be permitted as a hematopoietic stem cell (HSC) source on this protocol Patients who received organ or allogeneic bone marrow or peripheral blood stem cell transplants If post allogeneic SCT must not have less than % donor chimerism in either peripheral blood or bone marrow DONOR: Bone marrow will be the only allowed stem cell source Patients must have a related or unrelated peripheral blood stem cell donor that meet one of the following criteria: Bone marrow: > % donor T-cell chimerism in peripheral blood, obtained after weeks post-transplant; ANC > x E/L DONOR: must be capable of and consent or assent to donation of peripheral blood stem cells Any donor type (e.g., related, unrelated) or stem cell source (bone marrow, peripheral blood, cord blood). Have identified a backup cells source in case of engraftment failure. The source can be autologous, related or unrelated. A person (such as a haploidentical family member) or unit of cord blood must be identified as a source of back-up cells source in case of engraftment failure Diagnosis of AML and MDS according to World Health Organization (WHO) classification that underwent first allogeneic hematopoietic cell transplant (HSCT) with either peripheral blood or bone marrow as the source of the hematopoietic stem cells DONOR SELECTION: Not applicable; this protocol employs autologous transplantation, utilizing the patients own hematopoietic stem cells obtained from either the peripheral blood or bone marrow Hematopoietic stem cell source is either with peripheral blood, bone marrow or cord blood. No more than antigen mismatch at HLA-A, -B, -C, -DRB or -DQB locus for unrelated donor with peripheral blood and bone marrow as the hematopoietic stem cell source; and DONOR: Fit to receive G-CSF (filgrastim) and give peripheral blood stem cells (normal blood counts, normotensive, and no history of stroke) Must have donor peripheral blood stem cells mobilized by National Marrow Donor Program (NMDP) standards; no bone marrow donors DONOR: Donor should agree to undergo general anesthesia and bone marrow harvest collection if peripheral blood stem cell (PBSC) yield is inadequate or otherwise not transplantable for whatever reason DONOR: Donors >= years of age must be the same individual whose cells were used as the source for the patients original stem cell transplant Marrow is the preferred source of stem cells from the HLA-haploidentical donor, however, peripheral blood mononuclear cells (PBMC) could be used as stem cell source, after clearance with the Fred Hutchinson Cancer Research Center (FHCRC) principal investigator, in the case of difficulties or contraindications to bone marrow harvest from the donor DONOR: Marrow is the preferred source of stem cells from the HLA-haploidentical donor, however PBMC could be used as stem cell source, after clearance with the FHCRC principal investigator, in the case of difficulties or contraindications to bone marrow harvest from the donor Stem cell source Bone marrow (preferred source) OR peripheral blood stem cells of filgrastim [G-CSF]-stimulated donors OR cord blood Have identified a backup cells source in case of engraftment failure; the source can be autologous, related or unrelated DONOR: Donors able to undergo peripheral blood stem cell collection or bone marrow harvest Donor stem cell source can be either peripheral blood or bone marrow Cord blood as a donor source is not acceptable Have undergone first allogeneic hematopoietic stem cell transplantation (allo-HSCT) from any donor source using bone marrow, peripheral blood stem cells, or cord blood for hematologic malignancies. Recipients of nonmyeloablative and myeloablative conditioning regimens are eligible. HLA Matched Related Donor: G-CSF mobilized peripheral blood mononuclear cell (PBMC) only will be permitted as a hematopoietic stem cell (HSC) source on this protocol Back-up stem cell source DONOR: Peripheral blood stem cells (PBSC) only will be permitted as a HSC source on this protocol Have undergone first allo-HSCT from any donor source (matched unrelated donor, sibling, haploidentical) using bone marrow, peripheral blood stem cells, or cord blood for hematologic malignancies. Recipients of nonmyeloablative and myeloablative transplants are eligible. Patients receiving bone marrow or umbilical cord blood as a stem cell source may also be considered for enrollment with acknowledgement that if there is insufficient product available for DLI, the patient will receive azacitidine without DLI per standard-risk treatment DONOR: Meets standard institutional criteria for GCSF mobilized peripheral blood stem cell (PBSC) donation Use of cord blood as the source of hematopoietic cells is not allowed. DONOR: Donor must consent to peripheral blood stem cell (PBSC) mobilization with G-CSF (filgrastim) and apheresis F FLT CANDIDATE TRANSPLANT RECIPIENT: Donor who is willing to undergo bone marrow or stem cell harvest Participants must have a diagnosis of multiple myeloma documented by having > % plasma cells on bone marrow biopsy and/or monoclonal protein in blood and/or urine; all patients must have disease which is either stable or responsive after a minimum of cycles of conventional chemotherapy and slated to undergo autologous peripheral blood stem cell transplantation incorporating mobilization chemotherapy for peripheral blood stem cell collection DONOR: Only filgrastim (G-CSF) mobilized PBSC only will be permitted as a hematopoietic stem cell (HSC) source on this protocol DONOR: Marrow will be the only allowed hematopoietic stem cell source Have identified a back-up cell source in case of engraftment failure; the source can be autologous, related, or unrelated DONOR: Only G-CSF mobilized peripheral blood mononuclear cells (PBMC) only will be permitted as a hematopoietic stem cell (HSC) source on this protocol DONOR: Bone marrow is the preferred cell source Patients after allogeneic stem cell transplantation from a related or unrelated, HLA-matched or mismatched donor with the diagnosis of transplant related microangiopathy. Patients having received any of the following stem cell sources are eligible: G-CSF mobilized peripheral blood stem cells, bone marrow, umbilical cord blood. For Pre-allo Part A (before stem cell transplant): Partially matched donors (related or unrelated) and umbilical cord blood cells are excluded as the source of hematopoietic stem cells Prior autologous bone marrow or peripheral blood stem cell support within year Back-up stem cell source Have identified a back-up cells source in case of engraftment failure; the source can be autologous, related or unrelated Any diagnosis, donor or source of hematopoietic stem cells (HSC) is allowed, including donor leukocyte infusions (DLI) Stem cell source: bone marrow, peripheral blood stem cell Eligible patients will have one or more of the following donor stem cell sources:\r\n* Bone marrow\r\n* Placental blood (umbilical cord blood)\r\n* Cytokine mobilized peripheral blood Patients must have a plan to receive a CD-selected peripheral blood stem cell transplant with TBI-based conditioning DONOR: Must be willing and able to undergo peripheral blood stem cell (PBSC) collection Scheduled to undergo a hematopoietic stem cell transplant for any cancer or non-cancer illness from any autologous, related or unrelated donor source including bone marrow, peripheral blood progenitor cell, or umbilical cord blood Participants or their parents must consent to participation in active bone marrow and peripheral blood stem cell transplant protocols at the National Institutes of Health (NIH) Patients transplanted with hematopoietic stem cells from any source Peripheral blood stem cells must have been used as the stem cell source Must be candidates for peripheral blood stem cell transplants. DONOR: Unfit to undergo standard stem cell mobilization and apheresis e.g. abnormal blood counts, history of stroke, uncontrolled hypertension Donor must be willing to donate peripheral blood stem cells Peripheral blood stem cells, bone marrow, or umbilical cord blood may be used as the stem cell source If post allogeneic SCT must not have less than % donor chimerism in either peripheral blood or bone marrow Patients must have a related or unrelated peripheral blood stem cell donor as follows: Receiving first allogeneic HSCT (bone marrow, peripheral blood stem cell, or cord blood transplant) Patients must have a plan to receive a CD-selected peripheral blood stem cell graft