INCLUSION CRITERIA: Participants must have histologically or cytologically confirmed MDS according to 2016 WHO criteria  And:  have HR-MDS (R-IPSS >= 3.5) and received a minimum of 2 and maximum of 8 prior cycles for phase I and 4 for phase II of DNMTi therapy, or  have LR-MDS (R-IPSS <3.5),  and, at least one cytopenia:  granulocytes < 1.0 x 10^9/L and/or hemoglobin < 110 g/L with signs/symptoms of symptomatic anemia or transfusion-dependency platelets < 100 x 10^9/L  Age >=18 years  --Because no dosing or adverse event data are currently available on the use of BMS-986253 as monotherapy or in combination with DNMTi in participants <18 years of age, children are excluded from this study, but will be eligible for future pediatric trials.  ECOG performance status <=2 (Karnofsky >=60%). Life expectancy greater than 6 months.  Participants must have adequate organ function as defined below:  --total bilirubin <=1.5 X institutional upper limit of normal OR <=3 X institutional upper limit of normal in participants with Gilbert s syndrome (*except for participants with increased bilirubin levels attributed to intramedullary hemolysis, which will be allowable)  AST(SGOT)/ALT(SGPT) <=3 X institutional upper limit of normal OR <=5 X institutional upper limit of normal if related to disease specific cause creatinine clearance (by Cockcroft-Gault) >=60 mL/min/1.73 m^2 for participants with creatinine levels above institutional normal. The effects of BMS-986253 on the developing human fetus are unknown. For this reason and because DNMTi as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential (WOCBP) and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and up to 6 months after study completion and last dose of DNMTi. Ability of subject to understand and the willingness to sign a written informed consent document.  EXCLUSION CRITERIA:  For phase I: Participants with HR-MDS (R-IPSS >=3.5) that have not yet received or received less than 2 cycles of DNMTi therapy.  Participants with LR-MDS (R-IPSS <3.5) with the following characteristics that have not yet received or are still deriving benefit fromthe following standard of care therapies:  Hgb <10 g/dL, Epo level <500 mU/mL: Erythropoietin-stimulating agents (ESAs) MDS with del5q: Lenalidomide MDS with ringed sideroblasts (MDS-RS) with SF3B1 mutation: Luspatercept Participants with platelet transfusion-refractory thrombocytopenia, with inability to keep platelet threshold above 10K/mcL with transfusions or those with ongoing or uncontrolled hemorrhagic complications. Participants with clinically significant neutropenia, ANC<100, with frequent hospitalizations for infection (average >1 hospitalization per month in past 6 months) Participants who are receiving or have received any other investigational agents within 28 days before start of study  treatment.  History of allergic reactions attributed to compounds of similar chemical or biologic composition to DNMTi or other agents used in study. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. Pregnant women or women presently breast-feeding their children are excluded due to unknown risks to a developing fetus or infant. Any significant disease that, in the opinion of the investigator, may impair the participant s tolerance of study treatment. Active or uncontrolled autoimmune diseases requiring treatment. Chronic hepatitis B or C infection, because potential immune impairment caused by these disorders may diminish the effectiveness of this immunologic therapy. HIV-positive participants are ineligible because of the potential for decreased immune response. Presence of any other malignancy (except basal and squamous cell carcinoma of the skin, or stable chronic cancers on hormone or targeted therapy) for which participant received systemic anticancer treatment within 24 months prior to enrollment.