Could a lower dose of cyclophosphamide make stem cell transplants less risky?

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

* INCLUSION CRITERIA: Inclusion Criteria - Recipient * Patients must have a histologically or cytologically confirmed hematologic malignancy with standard indication for allogeneic hematopoietic cell transplantation limited to one of the following: * Acute myeloid leukemia (AML) of intermediate or adverse risk disease by the 2017 European LeukemiaNet criteria in first morphologic complete remission (\<5% blasts in the bone marrow, no detectable abnormal peripheral blasts, and no extramedullary disease) * AML of any risk in second or subsequent morphologic complete remission * B-cell acute lymphoblastic leukemia in first or subsequent complete remission * T-cell acute lymphoblastic leukemia with minimal residual disease detected after first line therapy and/or adverse genetics (no NOTCH1/FBXW7 mutation or presence of N/K-RAS mutation and/or PTEN gene alteration) * Myelodysplastic syndrome of intermediate or higher score by the Revised International Prognostic Scoring System (IPSS-R) * Primary myelofibrosis of intermediate-2 or higher risk by the DIPSS * Chronic myelomonocytic leukemia * Chronic myelogenous leukemia resistant to or intolerant of \>=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 * Chronic lymphocytic leukemia with 17p deletion and/or unmutated IgHV or refractory to 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 higher 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) * Age 15-65. Patients \<18 years old must be at least 50 kg. Note: Because patients 15-17 years old and \<50 kg are not able to be cared for on the adult oncology wards and by the investigative team, they are excluded. * At least one potentially suitable HLA-haploidentical donor. * Karnofsky performance score \>=60 * Adequate organ function defined as possessing all of the following: * Cardiac ejection fraction \>=45% by 2D ECHO; * Forced expiratory volume-1 (FEV-1), forced vital capacity (FVC), and diffusing capacity of the lung for carbon monoxide (DLCO) (corrected for hemoglobin) all of \>=50% predicted; * Estimated serum creatinine clearance of \>=60 ml/minute/1.73m\^2 calculated using eGRF in the clinical lab for adults and the Schwartz formula for pediatric subjects; * Total bilirubin \<=2X the upper limit of normal; * Alanine aminotransferase and aspartate aminotransferase \<=3X the upper limit of normal. * Myeloablative conditioning is toxic to the developing human fetus and is teratogenic. For this reason, the following measures apply: * Individuals of child-bearing potential (IOCBP) and participants who can father children must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for at least one year post-transplant. * IOCBP must have a negative serum or urine pregnancy test within 7 days prior to enrollment. * Ability of subject or Legally Authorized Representative to understand and the willingness to sign a written informed consent document. Pediatric patients (\<18 years of age) will provide assent, and the parent(s) or legal guardian(s) will provide informed consent. * Subjects requiring standard therapies to prepare for HCT should be referred in remission if possible. However, these diseases are often aggressive and require swift evaluation for HCT while concurrently attempting to establish disease control through the administration of standard therapies. If ongoing therapy for the underlying disease outside of the NIH is not in the best interest of the subject according to the clinical judgment of the PI, then the subject may receive up to 2 cycles of standard treatment for his/her underlying hematologic malignancy as a bridge to HCT on this protocol, prior to starting the research phase of the study. The subject must have a Karnofsky performance status of \>= 60% at the start of the first cycle to proceed. If it becomes apparent that the subject will not be able to proceed to HCT, then he/she must come off study. Subjects receiving standard therapy will be told about the therapy, associated risks, potential benefits, alternatives to the proposed therapy, and the availability of receiving the same treatment elsewhere, outside of a research protocol. EXCLUSION CRITERIA: Exclusion Criteria - Recipient * Patients who are receiving any other investigational agents. Prior experimental therapies must have been completed at least 4 weeks prior to the date of beginning conditioning. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection excluding controlled fungal infection on appropriate treatment, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, endocrinopathy (significant uncontrolled or untreated hypothyroidism, hyperthyroidism, or adrenal insufficiency), or active psychiatric illness/social situations that would limit compliance with study requirements * Prior myeloablative conditioning for autologous or allogeneic HCT. * An HLA-matched-sibling donor who is available and willing to donate bone marrow. Note: The patient must have access to HCT using this donor for this to be an exclusion criterion. * Individuals who are pregnant or who intend to become pregnant during the study are excluded because myeloablative conditioning is toxic to the developing fetus with the potential for teratogenic or abortifacient effects. * Nursing participants must be willing to discontinue nursing at the time of the study treatment initiation, as the potential for some of the study medications to be transmissible via nursing is unknown. * Active malignancy of non-hematopoietic type (excluding non-melanoma skin cancers) which is: metastatic, or relapsed/refractory to treatment, or locally advanced and not amenable to curative treatment, or limited disease treated with curative intent treatment within the last 2 years. This excludes non-melanoma skin cancers. * The severity of the hematologic malignancy does not warrant the potential toxicity of myeloablative allogeneic HCT as judged by the PI. INCLUSION CRITERIA: Inclusion Criteria - Related Donor * Related donor deemed suitable and eligible, and willing to donate, per clinical evaluations, who are additionally willing to donate blood, bone marrow, saliva, oral swab, and stool for research. Related donors will be evaluated in accordance with existing institutional Standard Policies and Procedures for determination of eligibility and suitability for clinical donation. * Ages \>= 12 years EXCLUSION CRITERIA: Exclusion Criteria - Related Donor -None