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) - Creatinine clearance of >= 60 mL/min per 24 hour urine test or the Cockcroft-Gault formula (within 30 days prior to day 1 of protocol therapy unless otherwise stated) - Left ventricular ejection fraction (LVEF) >= 50% - Note: To be performed within 30 days prior to day 1 of protocol therapy.

• - If able to perform pulmonary function tests: forced expiratory volume in 1 second (FEV1), forced vital capacity (FVC) and diffusion capacity of the lungs for carbon monoxide (DLCO) (diffusion capacity) >= 50% of predicted (corrected for hemoglobin) (within 30 days prior to day 1 of protocol therapy) - If unable to perform pulmonary function tests: O2 saturation > 92% on room air (within 30 days prior to day 1 of protocol therapy) - Seronegative for human immunodeficiency virus (HIV) antigen (Ag)/antibody (Ab) combo, hepatitis C virus (HCV), active hepatitis B virus (HBV) (surface antigen negative), and syphilis rapid plasma reagin (RPR) (within 30 days prior to day 1 of protocol therapy) - If positive, hepatitis C ribonucleic acid (RNA) quantitation must be performed OR.

• - If seropositive for HIV, HCV or HBV, nucleic acid quantitation must be performed.

Viral load must be undetectable.

• - Meets other institutional and federal requirements for infectious disease titer requirements.

• - Note: Infectious disease testing to be performed within 28 days prior to day 1 of protocol therapy.

• - Women of childbearing potential (WOCBP): negative urine or serum pregnancy test (within 30 days prior to day 1 of protocol therapy) - If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required.

• - Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 6 months after the last dose of protocol therapy.

• - Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for > 1 year (women only)

  Exclusion Criteria:

  - Prior allogeneic HCT.

• - Chemotherapy, radiation therapy, biological therapy, immunotherapy within 21 days prior to day 1 of protocol therapy.

• - Note: Conditioning regimen within 21 days prior to day 1 of protocol therapy is not considered as an exclusion criterion.

Patients on maintenance chemotherapy are not excluded.

• - Other investigational drugs for treatment of GVHD.

• - History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agents.

• - Psychological issues, no appropriate caregivers identified, or non-compliant to medication.

• - Clinically significant uncontrolled illness.

• - Uncontrolled infection (bacterial, viral, fungal) - Other active malignancy.

• - Females only: Pregnant or breastfeeding.

• - Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures.

- Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)

PRIMARY OBJECTIVES:

• I. Safety lead-in: Determine if shortening tacrolimus administration period to 60 days (day +65 post-hematopoietic cell transplantation [HCT]), when combined with post-transplant cyclophosphamide (PTCy) and itacitinib at a fixed dose level as graft-versus-host disease (GVHD) prophylaxis, is safe and effective after mobilized peripheral blood stem cell (PBSC) allogeneic hematopoietic cell transplantation (HCT) from a matched related/unrelated donor, as assessed by grade 3-4 GVHD as dose limiting toxicity.

• II. Following the safety lead-in, evaluate the efficacy of PTCy, itacitinib and tacrolimus GVHD prophylaxis, as assessed by 1-year GVHD-free relapse-free survival (GRFS).

SECONDARY OBJECTIVES:

• I. Evaluate the safety of this regimen by assessing: Ia.

Adverse events: type, frequency, severity, attribution, time course, duration. Ib. Complications including acute and chronic GVHD, infections and delayed engraftment.

• II. Estimate overall survival (OS), progression-free survival (PFS), cumulative incidences of relapse/disease progression, and non-relapse mortality (NRM) at 100 days, and 1-year post-transplant.

• III. Estimate rates of acute and chronic GvHD, infections, and neutrophil recovery.

EXPLORATORY OBJECTIVES:

• I. Donor cell engraftment will be assessed by count monitoring and short tandem repeat (STR) chimerism analysis on days +30 and day +100.

• II. Describe the kinetics of immune cell recovery.

• III. Evaluate patient's quality of life on day +100, 6 months and one-year post-HCT.

• IV. Pharmacokinetics: serial blood sampling will be done to evaluate the steady-state pharmacokinetics of itacitinib after PTCy.

• V. Describe the kinetics of GVHD biomarkers, JAK-related inflammatory cytokines and STAT phosphorylation.

• VI. Evaluate and describe the cytokine release syndrome (CRS) post-HCT by assessing the incidence, frequency, and severity of CRS.

• VII. Obtain a preliminary estimate of gut microbiome diversity at baseline (preferably before fludarabine administration), and then on days +14, +30, and +100.

OUTLINE: Patients undergo peripheral blood stem cell infusion on day 0. Patients receive cyclophosphamide intravenously (IV) once daily (QD) on days 3 and 4, itacitinib orally (PO) QD on days 5-100, and tacrolimus IV or PO on days 6-65. After completion of study treatment, patients are followed up at day 180 and 1 year.

Arms

Experimental: Prevention (PBSCs, cyclophosphamide, itacitinib, tacrolimus)

Patients undergo peripheral blood stem cell infusion on day 0. Patients receive cyclophosphamide IV QD on days 3 and 4, itacitinib PO QD on days 5-100, and tacrolimus IV or PO on days 6-65.

Interventions

Drug: - Cyclophosphamide

Given IV

Drug: - Itacitinib

Given PO

Procedure: - Peripheral Blood Stem Cell Transplantation

Undergo peripheral blood stem cell infusion

Other: - Quality-of-Life Assessment

Ancillary studies

Drug: - Tacrolimus

Given IV or PO