Adding Itacitinib to Cyclophosphamide and Tacrolimus for the Prevention of Graft Versus Host Disease in Patients Undergoing Hematopoietic Stem Cell Transplants

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study principal investigator (PI) approval * Age: =\< 80 years * Note: Patients \> 70 years of age must have Karnofsky performance status \>= 80 and HCT-comorbidity index (CI) =\< 2 * Karnofsky performance status \>= 70% * Patients with the following diagnosis, eligible to undergo allogeneic HCT from an 8/8 match related/unrelated donor (A, B, C, DR by high resolution typing) * Acute leukemias (acute myeloid leukemia \[AML\] or acute lymphoblastic leukemia \[ALL\]) in complete remission with bone marrow (BM) blast of \< 5% * Myelofibrosis (MF): Primary or secondary with high- or intermediate-2 risk per Dynamic International Prognostic Scoring System (DIPSS) * Myelodysplastic syndrome (blast \< 10%) * Myeloproliferative neoplasm (MPN) other than MF needing HCT * Chronic myelomonocytic leukemia (CMML) * Total bilirubin =\< 2 x upper limit of normal (ULN) (unless has Gilbert's disease) (within 30 days prior to day 1 of protocol therapy unless otherwise stated) * Serum glutamic-oxaloacetic transaminase (SGOT) and serum glutamate pyruvate transaminase (SGPT) \< 5 x ULN (within 30 days prior to day 1 of protocol therapy unless otherwise stated) * Creatini…