This research is being done to learn whether drug called itacitinib, which is a novel inflammation- and immune-lowering drug (immunosuppressant), can be given before and after non-myeloablative peripheral blood stem cell transplantation (PBSCT; also known as a 'mini' transplant) to help prevent certain complications such as cytokine release syndrome (CRS) for patients with blood cancers, using peripheral blood from a relative. The investigators will also examine if by using itacitinib the investigators can reduce the duration of MMF (other immune suppressive drug administration posttransplant).

The NMA PBSC haplo transplant is associated with a higher risk of morbidity and mortality from the cytokine (IL-6 and others)-driven CRS and perhaps higher incidence of acute and chronic GVHD compared to bone marrow (BM) haplo allografting with post-transplant cyclophosphamide (PTCy). Notably, severe CRS (grade 3 and higher) appears to be more common in older patients (≥ 60 years) and is associated with significantly higher non-relapse mortality (NRM) in this patient group. Itacitinib has demonstrated safety, tolerability, ability to inhibit cytokines, including IL-6. Data also suggest that itacitinib can be administered safely in peri- and post-transplant period in the setting of Posttransplant CY immune prophylaxis and haploPBSCT with no evidence of delayed engraftment or delayed count recovery, with significant reduction in CRS compared to historical control, and a low rate of aGVHD, cGVHD, and NRM, and with no increase in relapse risk. Thus, the investigators propose a clinical study in which itacitinib will be used prophylactically in recipients age 60 years and older to prevent development of severe CRS, reduce severe CRS-associated NRM, and the incidence of severe GVHD, thus allowing further reduction in posttransplant immunosuppression therapy after PTCy-based NMA related partially-mismatched PB allografting.

Inclusion Criteria:

• Presence of a suitable related, HLA-haploidentical (partially mismatched) stem cell donor.

• Eligible diagnoses:

  1. Acute leukemias in complete remission with minimal residual disease
  2. Myelodysplastic syndrome (MDS) with at least one poor-risk feature
  3. Chronic myelomonocytic leukemia with at least one poor-risk feature
  4. T-cell PLL in PR or better prior to transplantation.
  5. Tyrosine kinase-refractory CML in first chronic phase, TKI-intolerant CML in first chronic phase, or CML in second or subsequent chronic phase.
  6. Philadelphia chromosome negative myeloproliferative disease (including myelofibrosis)
  7. Multiple myeloma or plasma cell leukemia with a PR or better to the last treatment regimen

• Age ≥ 60 years.

• Adequate end-organ function as measured by:

  1. Left ventricular ejection fraction ≥ 35% or shortening fraction > 25%
  2. Bilirubin ≤ 3.0 mg/dL (unless due to Gilbert's syndrome or hemolysis), and ALT and AST ≤ 5 x ULN
  3. FEV1 and FVC ≥ 40% of predicted

• ECOG performance status ≤ 2 or Karnofsky score ≥ 60

Exclusion Criteria:

• No active extramedullary leukemia or known active CNS involvement by malignancy.
• Any previous autologous HSCT must have occurred at least 3 months prior to start of conditioning.
• No previous allogeneic HSCT.
• Not pregnant or breast-feeding
• No uncontrolled infection.
• No known HIV infection.
• No active replicating HBV or HCV infection detected by PCR that requires treatment or at risk for HBV reactivation (positive HBsAg)