Phase I/II Study to Reduce Post-transplantation Cyclophosphamide Dosing for Older or Unfit Patients Undergoing Bone Marrow Transplantation for Hematologic Malignancies

Background: Certain blood cancers can be treated with blood or bone marrow transplants. Sometimes the donor cells attack the recipient's body, called graft-versus-host disease (GVHD). The chemotherapy drug cyclophosphamide helps reduce the risk and severity of GVHD. Researchers want to learn if using a lower dose of cyclophosphamide may reduce the drug's side effects while maintaining its effectiveness. Such an approach is being used in an ongoing clinical study at the NIH with promising results, but this approach has not been tested for transplants using lower doses of chemotherapy/radiation prior to the transplant. Objective: To learn if using a lower dose of cyclophosphamide will help people have a successful transplant and have fewer problems and side effects. Eligibility: Adults ages 18-85 who have a blood cancer that did not respond well to standard treatments or is at high risk for relapse without transplant, and their donors. Design: Participants may be screened with the following: Medical history Physical exam Blood and urine tests Heart and lung tests Body imaging scans (they may get a contrast agent) Spinal tap Bone marrow biopsy Participants will be hospitalized for 4-6 weeks. They will have a central venous catheter placed in a chest or neck vein. It will be used to give medicines, transfusions, and the donor cells, and to take blood. In the week before transplant, they will get 2 chemotherapy drugs and radiation. After the transplant, they will get the study drug for 2 days. They will take other drugs for up to 2 months. Participants must stay near NIH for 3 months after discharge for weekly study visits. Then they will have visits every 3-12 months until 5 years after transplant. Participants and donors will give blood, bone marrow, saliva, cheek swab, urine, and stool samples for research.

-INCLUSION CRITERIA - Recipient 1. Subjects must have a histologically or cytologically confirmed hematologic malignancy with standard indication for allogeneic hematopoietic cell transplantation including, but not limited to, one of the following: * Acute myeloid leukemia in morphologic complete remission (\=3 tyrosine kinase inhibitors or with history of accelerated phase or blast crisis * B-cell lymphoma including Hodgkin lymphoma that has relapsed within 1 year of completion of primary treatment, after autologous transplantation or has progressed through at least 2 lines of therapy * Chronic lymphocytic leukemia with 17p deletion and/or unmutated IgHV or refractory or intolerant of both BTK and PI3K inhibitors * Mature T or NK neoplasms as defined in the WHO guidelines of sufficient type and severity for allogeneic HCT based on the Prognostic Index for T-cell lymphoma (PIT) score of low-intermediate risk or higher60 or on recently published clinical practice guidelines * Hematologic malignancy of dendritic cell or histiocytic cell type * Multiple myeloma, stage III, relapsing after therapy with both a proteasome inhibitor and an immunomodulatory drug (IMiD) 2. Age 60-85 years, or age 18-60 years and unfit for myeloablative conditioning. Reasons for unfitness for myeloablative conditioning include: * Prior myeloablative HCT * Prior exposure to inotuzumab, gemtuzumab, or other agent that increases the risk for sinusoidal obstruction syndrome. * Significant organ dysfunction (e.g., creatinine or liver enzymes above the upper limit of normal or EGFR \=35%; * Forced expiratory volume-1, forced vital capacity, and diffusing capacity of the lung for carbon monoxide (corrected for hemoglobin) all of \>=40% predicted; * Serum creatinine clearance of \>=45 ml/minute calculated using the Cockcroft-Gault equation; * Total bilirubin \=12) and unrelated (age \>=18) donors deemed eligible (i.e., evaluated at NIH in accordance with existing institutional Standard Policies and Procedures or evaluated per the standards required by the IRB of the National Marrow Donor Program or applicable registry), and willing to donate research samples will be included. EXCLUSION CRITERIA - Donor: None