CLAG-M or FLAG-Ida Chemotherapy and Reduced-Intensity Conditioning Donor Stem Cell Transplant for the Treatment of Relapsed or Refractory Acute Myeloid Leukemia, Myelodysplastic Syndrome, or Chronic Myelomonocytic Leukemia

Inclusion Criteria: * Age \>= 18 years with an Hematopoietic Cell Transplantation-Comorbidity Index (HCT-CI) =\< 5 for patients over 60 years -(Enrollment of patients \>= 75 years of age will require case presentation at the transplant Patient Care Conference (PCC) and approval by consensus) * 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 other therapies), or is in untreated or unsuccessfully treated first or subsequent 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 relapsed or refractory acute leukemia of ambiguous lineage (acute undifferentiated leukemia, mixed phenotype acute leukemia) that is either primary refractory or is in untreated or unsuccessfully treated first or subsequent relapse are also 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 follow…