• Patients in 1st or 2nd remission with acute myeloid leukemia (AML) or acute lymphoblastic leukemia (ALL), who are eligible for stem cell transplant. Remission defined as no circulating blasts, \< 5% blasts in the bone marrow, normalization of previously detected cytogenetic abnormalities, no extramedullary disease

• High risk myelodysplastic syndrome (MDS)

‣ Intermediate II and high risk by International Prognostic Scoring System (IPSS)

⁃ Intermediate, high, or very high by World Health Organization (WHO) classification-based Prognostic Scoring System (WPSS)

⁃ Transfusion dependent

⁃ Therapy-related MDS or MDS evolved from previous hematological disorder (excepting myelofibrosis)

• Patients with chronic myelomonocytic leukemia (CMML) are allowed to be enrolled

• Patients with MDS that has evolved to AML must be in remission

• Patients must not be eligible for full ablative regimens by the attending physician

• Patients with AML or MDS arising from myeloproliferative neoplasm can be enrolled after principal investigator (PI) approval on case to case basis, depends on the spleen size and degree of bone marrow fibrosis

• Performance status of \>= 70% on the Karnofsky scale

• Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for six months following duration of study participation; should a woman become pregnant or suspect she is pregnant while participating on the trial, she should inform her treating physician immediately

• Bone marrow and peripheral blood studies must be available for confirmation of diagnosis; cytogenetics, flow cytometry, and molecular studies (such as Flt-3 status) will be obtained as per standard practice

• Bone marrow aspirates/biopsies should be performed within 28 (+ 4 day window) days from registration to confirm disease remission status

• A pretreatment measured creatinine clearance (absolute value) of \>= 60 mL/minute

• Patients must have a serum bilirubin =\< 2.0 mg/dl

• Patients must have serum glutamic oxaloacetic transaminase (SGOT) and serum glutamate pyruvate transaminase (SGPT) =\< 2.5 times the institutional upper limit of normal

• Ejection fraction measured by echocardiogram or multi gated acquisition scan (MUGA) \> 50%

• Diffusing capacity of the lung for carbon monoxide (DLCO) or forced expiratory volume in 1 second (FEV1) \> 45% predicted

• Availability of a human leukocyte antigen (HLA) matched (6/6) sibling donor or 8/8 matched unrelated donor; Donors with mismatch at HLA-A, HLA-B, HLA-C, and HLA-DR will be reviewed by matched unrelated donor (MUD) committee and allowed if their mismatch with the recipient does not require additional GVHD prophylaxis (other than tacrolimus and sirolimus), donors with mismatch at HLA-DQ or HLA-DPB are eligible; donor evaluation according to City of Hope (COH) standard operating procedure (SOP)

• Donor stem cell source can be either peripheral blood or bone marrow

• All patients must have a psychosocial evaluation prior to transplant as per COH SOP

• All subjects must have the ability to understand and the willingness to sign a written informed consent

• ALL or AML patients who received chemotherapy (induction or consolidation) can proceed to transplant once bone marrow cellularity is \> 10 % with no evidence of leukemia