Study of Nonmyeloablative Peripheral Blood Stem Cell Transplant With High-dose Posttransplantation Cyclophosphamide in Hematopoietic Malignancies Including Those That Are Challenging to Engraft

Inclusion Criteria: The following are eligibility for study entry and transplantation. * Presence of a suitable related, HLA-haploidentical or HLA-matched stem cell donor * The donor and recipient must be identical at least one allele of each of the following genetic loci: HLA-A, HLA-B, HLA-Cw, HLA-DRB1, and HLA-DQB1. A minimum match of 5/10 is therefore required for related donors, and will be considered sufficient evidence that the donor and recipient share one HLA haplotype. * Eligible diagnoses: * Myelodysplastic syndrome (MDS) including chronic myelomonocytic leukemia \[CMML\] with at least one poor risk factor * No active extramedullary leukemia or known active CNS involvement by malignancy. Such disease treated into remission is permitted. * Any previous autologous HSCT must have occurred at least 3 months prior to start of conditioning * No previous allogeneic HSCT * Adequate end-organ function Note: Infection is permitted if there is evidence of response to medication. Eligibility of HIV infected patients will be determined on a case-by-case basis. * ECOG performance status \< 2 or Karnofsky or Lansky score \> 60. * Age \> 18 years and older. * Not pregnant or breast-feeding. * No uncontrolled infection. Eligible diagnoses: * Myelodysplastic syndrome (MDS) including chronic myelomonocytic leukemia \[CMML\] with at least one of the following poor-risk features * SLL or CLL with 17p deletion, or with progression \< 6 months after second or greater treatment regimen. Must have the following to be an acceptable candidate as well: * \< 20% of bone marrow cellularity involved by SLL/CLL (to lower risk of graft rejection) * No lymph nodes \> 5 cm in any dimension * No massive splenomegaly, defined as \> 6 cm below the left costal margin * T-cell PLL in PR or better prior to transplantation. Must also have \< 20% of bone marrow cellularity involved by PLL (to lower risk of graft rejection). * Interferon- or tyrosine kinase-refractory CML in first chronic phase, TKI-intolerant CML in first chronic phase, or CML in second or subsequent chronic phase * Philadelphia chromosome negative myeloproliferative disease (including myelofibrosis) o Intermediate-2 or High risk score by DIPSS Plus is required for a diagnosis of myelofibrosis * Multiple myeloma or plasma cell leukemia with a PR or better to the last treatment regimen, based on the International Myeloma Working Group (IMWG) criteria.49 * Hematologic malignancy in complete remission with minimal residual disease (MRD) non detectable OR detectable by conventional cytogenetics, FISH, flow cytometry, or molecular testing or hematologic malignancies in partial remission Donor eligibility * Donors must be either: * HLA-haploidentical or HLA-identical relatives of the patient based on allele or allele group level typing as defined in Section 4.1. * Medically fit to and willing to donate * Lack of recipient anti-donor HLA antibody * Has not donated blood products to patient Exclusion Criteria: * Any individual that does not meet the eligibility criteria for transplantation or donor eligibility will not be a part of this trial.