PRIMARY OBJECTIVE:

I. Evaluate the efficacy of the haploidentical hematopoietic cell transplantation (haploHCT) total marrow and lymphoid organ irradiation (TMLI), with high dose post-transplant cyclophosphamide (PTCy) as graft-versus host disease (GvHD) prophylaxis, as assessed by 1-year graft versus (vs) host disease-free relapse-free survival (GRFS) rate in each arm (Arm

1. patients with acute myeloid leukemia [AML] or myelodysplastic syndrome [MDS] and Arm B: Patients with acute lymphoblastic leukemia [ALL]).

SECONDARY OBJECTIVES:

I. Estimate overall survival (OS), cumulative incidences of relapse/disease progression, and non-relapse mortality (NRM) in each arm at 100 days, and 1 year post-transplant.

II. Estimate rate of relapse and non-relapse mortality (NRM) at 1 year post-transplant.

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

IV. Describe and characterize cytokine release syndrome (CRS) post-haploidentical HCT with TMLI as conditioning regimen and PTCy as GvHD prophylaxis as assessed by incidence, frequency and severity.

V. Further evaluate the safety of this regimen by assessing:

Va. Adverse events: type, frequency, severity, attribution, time course, duration.

Vb. Complications: including acute/chronic GVHD, infection and delayed engraftment.

EXPLORATORY OBJECTIVES:

I. Characterize minimal residual disease from bone marrow aspirates and investigate the possible association between TMLI-based regimen and patient's disease status.

II. Describe the kinetics of immune cell recovery. III. Describe the kinetics of serum pro-inflammatory cytokines and GvHD biomarkers.

IV. Longitudinal and spatial assessment of TMLI effect on bone marrow environment.

V. Cellular and molecular assessment of TMLI effect on bone marrow environment and TMLI effect on the engraftment and disease relapse.

CONDITIONING: Patients receive fludarabine intravenously (IV) once daily (QD) on days -7 to -5, and undergo TMLI twice daily (BID) on days -4 to 0 in the absence of disease progression or unacceptable toxicity.

TRANSPLANT: Patients undergo hematopoietic cell transplantation on day 0.

GVHD PROPHYLAXIS: Patients receive cyclophosphamide IV QD on days 3-4 in the absence of disease progression or unacceptable toxicity. Beginning on day 5, patients also receive granulocyte colony stimulating factor and tacrolimus/mycophenolate mofetil per institutional standard.

After completion of study treatment, patients are followed up twice weekly for the first 100 days post-transplant, twice monthly until 6 months post-transplant, monthly until patient discontinues immunosuppressive therapy, and then yearly for 2 years.