This randomized phase II trial studies azacitidine with or without entinostat to see how well they work compared to azacitidine alone in treating patients with myelodysplastic syndromes, chronic myelomonocytic leukemia, or acute myeloid leukemia. Drugs used in chemotherapy, such as azacitidine, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Entinostat may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Giving azacitidine together with entinostat may work better in treating patients with myelodysplastic syndromes, chronic myelomonocytic leukemia, or acute myeloid leukemia.

PRIMARY OBJECTIVES:

I. To estimate the overall response rate (complete, partial, and hematologic improvement-major by International Working Group [IWG] criteria) in response to azacitidine and entinostat.

II. To estimate the major response rate (complete and partial responses by the IWG response criteria) to a 10-day regimen of azacitidine and to the same regimen of azacitidine in combination with entinostat administered orally on days 3 and 10 of each cycle in patients with de novo myelodysplastic syndromes (MDS), chronic myelomonocytic leukemia (CMMoL) (dysplastic) and acute myeloid leukemia with trilineage dysplasia (AML-TLD), as well as in patients with treatment-induced MDS, CMMoL (dysplastic) and AML-TLD.

SECONDARY OBJECTIVES:

I. To evaluate the toxicity of azacitidine and entinostat in this patient population.

II. To identify changes in gene promoter methylation and gene expression which may be associated with response to azacitidine and entinostat.

III. To identify other molecular mechanisms (such as deoxyribonucleic acid [DNA] damage) which may be associated with response to azacitidine and entinostat.

OUTLINE: Patients are randomized to 1 of 2 treatment arms.

ARM A: Patients receive azacitidine subcutaneously (SC) once daily (QD) on days 1-10.

ARM B: Patients receive azacitidine as in Arm A and entinostat orally (PO) on days 3 and 10.

In both arms, treatment repeats every 28 days for 6-24 courses in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up for 5 years.

Inclusion Criteria:

• The following diagnoses will be eligible for this study:
• Myelodysplastic syndromes: the diagnosis of MDS must be confirmed by a bone marrow aspirate and/or biopsy within two weeks prior to registration; NOTE: blast count must be < 20%; patients with any International Prognostic Score (IPSS) are eligible; patients with low or intermediate (INT)-1 IPSS must have a platelet count < 50,000/mm^3 and/or absolute neutrophil count (ANC) < 500/mm^3 within seven days prior to registration
• Chronic myelomonocytic leukemia (dysplastic subtype): the diagnosis of CMMoL must be confirmed by a bone marrow aspirate and/or biopsy within two weeks prior to registration; patients with CMMoL must have a WBC < 12,000/mm^3, documented within 4 weeks prior to study entry (two sets of counts that are 2 weeks apart will be taken)
• Acute myeloid leukemia with multilineage dysplasia: the diagnosis of AML-TLD must be confirmed by a bone marrow aspirate and/or biopsy within two weeks prior to registration; NOTE: there must be evidence of >= 20% blasts on the review of the bone marrow aspirate and/or biopsy; AML-TLD will be interpreted to include patients formerly diagnosed by French-American-British (FAB) criteria as refractory anemia with excess blasts in transformation (RAEB-t), as well as patients with no history of antecedent hematologic disorder who have AML which meets criteria for AML-TLD by World Health Organization (WHO) criteria; patients with AML-TLD must have a white blood cell (WBC) =< 30,000/mm^3 documented within 4 weeks prior to study entry (two sets of counts that are 2 weeks apart will be taken); patients whose WBC has doubled within this period of time and is greater than 20,000/mm^3 at the time of screening will not be eligible
• Women must not be pregnant or breast-feeding; all females of childbearing potential must have a blood test or urine study within two weeks prior to registration to rule out pregnancy
• Women of childbearing potential and sexually active males must be strongly advised to use an accepted and effective method of contraception
• Patient must have Eastern Cooperative Oncology Group (ECOG) performance status between 0-2
• Patient must have no prior treatment with azacitidine, decitabine or entinostat
• Patients must not have active infections at the time of registration
• Serum creatinine < 2.0 mg/dL; test must be done within seven days prior to registration
• Total serum bilirubin within institutional limits unless due to intra- or extramedullary hemolysis or Gilbert's syndrome; test must be done within seven days prior to registration
• Aspartate transaminase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) and alanine transaminase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x institutional upper limit of normal (ULN); tests must be done within seven days prior to registration
• Patients must not have received any AML induction chemotherapy or stem cell transplantation; any other treatment for their disease, including hematopoietic growth factors may not be given, within three weeks prior to registration, and should have recovered from all toxicities of prior therapy (to grade 0 or 1)
• Patients must have no clinical evidence of central nervous system (CNS) or pulmonary leukostasis, disseminated intravascular coagulation, or CNS leukemia
• Patients must have no serious or uncontrolled medical conditions
• Patients who have therapy-induced MDS, CMMoL (dysplastic) and AML-TLD are eligible and will be treated as separate cohorts from the patients with de novo MDS, CMMoL (dysplastic) and AML-TLD
• Patients should have a life expectancy of at least six months
• Patients must not have advanced malignant hepatic tumors
• Patients must not have a known hypersensitivity to azacitidine or mannitol
• Southwest Oncology Group (SWOG) ONLY: all SWOG patients must be registered on SWOG-9007 ("Cytogenetic Studies in Leukemia Patients"); collection of the pretreatment bone marrow specimen (or of peripheral blood if the marrow is not aspirable) must be completed within 28 days before registration; the pretreatment specimen must be submitted to a SWOG-approved cytogenetics laboratory as described in protocol SWOG-9007; note that submission of bone marrow cytogenetic studies are required to calculate the IPSS score (stratification issue); in addition, cytogenetic response will be measured at follow-up requiring a second cytogenetic study at the end of protocol treatment; NOTE: In addition to SWOG-9007, SWOG patients must be offered participation in S9910, the leukemia centralized reference laboratories and tissue repositories ancillary study; If consent is given, collection of pretreatment blood and/or marrow specimens must be completed within 14 days prior to registration. If the patient consents to participate in S9910, pretreatment specimens of marrow and/or peripheral blood must be submitted to the Southwest Oncology Group Myeloid Repository at the University of New Mexico for cellular and molecular studies; S9910 also requests submission of remission and relapse specimens