Nivolumab and Ipilimumab After Donor Stem Cell Transplant in Treating Patients With High Risk Refractory or Relapsed Acute Myeloid Leukemia or Myelodysplastic Syndrome

Inclusion Criteria: * Patients with evidence of relapsed or refractory AML or MDS following allogeneic stem cell transplantation * Patients must have received preparative regimens to include either busulfan- or melphalan-based regimens * Patient must have achieved myeloid engraftment as defined by an absolute neutrophil count \>= 500 micro/L on 3 consecutive days * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Total bilirubin =\< 2 times upper limit of normal (x ULN) (=\< 3 x ULN if considered to be due to Gilbert's syndrome) * Aspartate aminotransferase or alanine aminotransferase =\< 2.5 x ULN * Serum creatinine =\< 2 x ULN or glomerular filtration rate (GFR) \>= 50 * Patients must provide written informed consent * The interval from the infusion of stem cells to time of initiation of nivolumab or ipilimumab will be at least 6 weeks (42 days) * Females must be surgically or biologically sterile or postmenopausal (amenorrheic for at least 12 months) or if of childbearing potential, must have a negative serum or urine pregnancy test within 72 hours before the start of the treatment * Women of childbearing potential must agree to use an adequate method of contraception during the study and until 3 months after the last treatment. Males must be surgically or biologically sterile or agree to use an adequate method of contraception during the study until 3 months after the last treatment Exclusion Criteria: * Patients with known allergy or hypersensitivi…