Inclusion Criteria:

          -  Hematopoietic Cell Transplantation-Comorbidity Index (HCT-CI) =< 5 for patients over
             60 years

          -  Acute myeloid leukemia (AML) (2016 World Health Organization [WHO] criteria) that is
             either primary refractory (as defined by failure of 2 cycles of 7+3-like chemotherapy,
             1 cycle of high-dose cytarabine-based chemotherapy, or at least 2 cycles of venetoclax
             in combination with either low-dose cytarabine or an azanucleoside), or is in early
             (remission duration =< 6 months) untreated relapse. Patients in morphological
             remission (i.e. < 5% blasts in the bone marrow) but evidence of minimal residual
             disease (MRD) by multiparameter flow cytometry, cytogenetics/fluorescence in situ
             hybridization (FISH), or molecular means will be eligible for trial participation.
             Patients with refractory acute leukemia of ambiguous lineage (acute undifferentiated
             leukemia, mixed phenotype acute leukemia) are eligible

          -  Subjects with previously treated myelodysplastic syndrome (MDS) and chronic
             myelomonocytic leukemia (CMML), defined as prior treatment with at least one
             hypomethylating agent (HMA; azacitidine and/or decitabine) whose disease progressed,
             relapsed, or was refractory to HMA treatment as follows: patients who have failed at
             least 6 cycles of azacitidine or 4 cycles of decitabine

          -  The use of hydroxyurea prior to initiation of study treatment is allowed. Patients
             with symptoms/signs of hyperleukocytosis, WBC > 100,000/uL or with concern for other
             complications of high tumor burden (e.g. disseminated intravascular coagulation) can
             be treated with leukapheresis or may receive up to 2 doses of cytarabine (up to 500
             mg/m^2 per dose) prior to start of study treatment

          -  Karnofsky score >= 70; Eastern Cooperative Oncology Group (ECOG) 0-1

          -  Adequate cardiac function defined as absence of decompensated congestive heart failure
             and/or uncontrolled arrhythmia and left ventricular ejection fraction >= 45%

          -  Bilirubin =< 2.5 x institutional upper limit of normal unless elevation is thought to
             be due to hepatic infiltration by AML, Gilbert's syndrome, or hemolysis

          -  Adequate pulmonary function defined as absence of oxygen (O2) requirements and either
             carbon monoxide diffusing capability test (DLCO) correct >= 70% mmHg or DLCO corrected
             60-69% mmHg and partial pressure of oxygen (pO2) >= 70 mmHg

          -  Serum creatinine =< 1.5 mg/dL

          -  Prior autologous HCT is permissible if relapse occurred > 3 months but =< 6 months
             after HCT

          -  Prior TBI-containing allogeneic HCT up to 3 Gy is permissible if > 6 months after HCT

          -  A human leukocyte antigen (HLA)-matched or near-matched related or unrelated donor for
             collection of stimulated peripheral blood stem cells must be identified and readily
             available

          -  Women of childbearing potential and men must agree to use adequate contraception
             beginning at the signing of the consent until at least 12 months post-transplant

          -  Patients may have previously received chemotherapy with a mitoxantrone- or
             cladribine-based regimen for MDS or AML. If the patient has received CLAG-M before and
             has been sensitive to this regimen, eligibility will be determined on a case-by-case
             basis by the study principal investigator (PI)

          -  Ability to understand and sign a written informed consent document (or legal
             representative)

          -  DONOR: Patients must have an HLA-matched related donor or an HLA-matched unrelated
             donor who meets standard SCCA and/or National Marrow Donor Program (NMDP) or other
             donor center criteria for peripheral blood stem cell (PBSC) donation as follows:

               -  Related donor: related to the patient and genotypically or phenotypically
                  identical for HLA-A, B, C, DRB1 and DQB1. Phenotypic identity must be confirmed
                  by high-resolution typing

               -  Unrelated donor:

                    -  Matched for HLA-A, B, C, DRB1 and DQB1 by high resolution typing; OR

                    -  Mismatched for a single allele without antigen mismatching at HLA-A, B, or C
                       as defined by high resolution typing but otherwise matched for HLA-A, B, C,
                       DRB1 and DQB1 by high resolution typing

                    -  Donors are excluded when preexisting immunoreactivity is identified that
                       would jeopardize donor hematopoietic cell engraftment. The recommended
                       procedure for patients with 10 of 10 HLA allele level (phenotypic) match is
                       to obtain panel reactive antibody (PRA) screens to class I and class II
                       antigens for all patients before HCT. If the PRA shows > 10% activity, then
                       flow cytometric or B and T cell cytotoxic cross matches should be obtained.
                       The donor should be excluded if any of the cytotoxic cross match assays are
                       positive. For those patients with an HLA class I allele mismatch, flow
                       cytometric or B and T cell cytotoxic cross matches should be obtained
                       regardless of the PRA results. A positive anti-donor cytotoxic crossmatch is
                       an absolute donor exclusion

                    -  Patient and donor pairs homozygous at a mismatched allele in the graft
                       rejection vector are considered a two-allele mismatch, i.e., the patient is
                       A*0101 and the donor is A*0102, and this type of mismatch is not allowed

        Exclusion Criteria:

          -  Patients >= 18 years being treated at Seattle Children's Hospital

          -  Active central nervous system (CNS) disease

          -  Concomitant illness associated with a likely survival of < 1 year

          -  Active systemic fungal, bacterial, viral, or other infection, unless disease is under
             treatment with anti-microbials and/or controlled or stable. Patients with fever
             thought to be likely secondary to myeloid malignancy are eligible

          -  Known hypersensitivity or contraindication to any study drug used in this trial

          -  Pregnancy or lactation

          -  Concurrent treatment with any other approved or investigational anti-leukemia agent