Inclusion Criteria:

* Patients must have AML, ALL, high-risk MDS, or MPAL (also known as biphenotypic) meeting one of the following descriptions:

* AML, ALL, or MPAL in first remission with evidence of measurable residual disease (MRD) by flow cytometry;
* AML, ALL, or MPAL beyond first remission (i.e., having relapsed at least one time after achieving remission in response to a treatment regimen);
* AML, ALL, or MPAL representing primary refractory disease (i.e., having failed to achieve remission at any time following one or more prior treatment regimens);
* AML evolved from myelodysplastic or myeloproliferative syndromes;
* MDS expressed as refractory anemia with excess blasts (RAEB)
* Chronic myelomonocytic leukemia (CMML) by French-American-British (FAB) criteria.
* Patients not in remission must have CD45-expressing leukemic blasts. Patients in remission do not require phenotyping and may have leukemia previously documented to be CD45 negative (because in remission patients, virtually all antibody binding is to non-malignant cells which make up \>= 95% of nucleated cells in the marrow).
* Patients must be \>= 18 and =\< 75 years of age.
* Patients should have a circulating blast count of less than 10,000/mm\^3 (control with hydroxyurea or similar agent is allowed).
* Patients must have an estimated creatinine clearance greater than 50/ml per minute by the following formula (Cockcroft-Gault). Serum creatinine value must be within 28 days prior to registration.
* Bilirubin \< 2 times the upper limit of normal.
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 2 times the upper limit of normal.
* Eastern Cooperative Oncology Group (ECOG) \< 2 or Karnofsky \>= 70.
* Patients must be free of uncontrolled infection.
* Patients with prior non-myeloablative or reduced-intensity conditioning allogeneic-HCT must have no evidence of ongoing GVHD and be off all immunosuppression for at least 6 weeks at time of enrollment.
* Patients must have a related donor who is identical for one HLA haplotype and mismatched at the HLA-A, -B or DRB1 loci of the unshared haplotype with the exception of single HLA-A, -B or DRB1 mismatches.
* DONOR: Donors must meet HLA matching criteria as well as standard Seattle Cancer Care Alliance (SCCA) criteria for PBSC or bone marrow donation. Preference should be given to donors who are mismatched at the HLA-A, -B and -DRB1 loci.

Exclusion Criteria:

* Patients may not have symptomatic coronary artery disease and may not be on cardiac medications for anti-arrhythmic or inotropic effects.
* Left ventricular ejection fraction \< 45%.
* Corrected diffusion capacity of the lung for carbon monoxide (DLCO) \< 35% or receiving supplemental continuous oxygen. When pulmonary function tests (PFTs) cannot be obtained, the 6-minute walk test (6MWT, also known as exercise oximetry) will be used: Any patient with oxygen saturation on room air of \< 89% during a 6MWT will be excluded
* Liver abnormalities: fulminant liver failure, cirrhosis of the liver with evidence of portal hypertension, alcoholic hepatitis, esophageal varices, hepatic encephalopathy, uncorrectable hepatic synthetic dysfunction as evidenced by prolongation of the prothrombin time, ascites related to portal hypertension, bacterial or fungal liver abscess, biliary obstruction, chronic viral hepatitis, or symptomatic biliary disease.
* Patients who are known to be seropositive for human immunodeficiency virus (HIV).
* Perceived inability to tolerate diagnostic or therapeutic procedures.
* Active central nervous system (CNS) leukemia at time of treatment.
* Patients with prior myeloablative allogeneic-HCT.
* Women of childbearing potential who are pregnant (beta human chorionic gonadotropin \[B-HCG\]+) or breast feeding.
* Fertile men and women unwilling to use contraceptives during and for 12 months post-transplant.
* Inability to understand or give an informed consent.
* Allergy to murine-based monoclonal antibodies.
* Known contraindications to radiotherapy.