Patients with secondary AML are eligible for enrollment onto the trial; secondary AML is defined as AML that has developed in a person with a history of antecedent blood count abnormalities, or myelodysplastic syndrome (MDS), or a myeloproliferative disorder (excluding chronic myeloid leukemia); or a history of prior chemotherapy or radiation therapy for a disease other than AML* NOTE: Prior therapy of MDS with decitabine, low-dose cytarabine, or azacitidine is excluded The following malignancies will be considered eligible if progressive or persistent:* Chronic lymphocytic leukemia (CLL)* Non-Hodgkin lymphoma (NHL)* Hodgkin lymphoma (HL)* Multiple myeloma (MM)* Acute leukemia (acute myeloid leukemia [AML], acute lymphoblastic leukemia [ALL])* Myelodysplastic syndrome (MDS)* Myeloproliferative neoplasms (MPN)* Chronic myeloid leukemia (CML) Patients with myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) or with features suggestive of MDS/AML Patients must have one of the following, histologically or cytologically confirmed:* Acute myeloid leukemia (AML) [non- acute promyelocytic leukemia (APL) AML]** If previously treated:*** AML that is relapsed or refractory to at least one prior line of therapy** If previously untreated, must meet all of the following:*** >= 60 years of age*** Secondary or therapy-related AML*** Does NOT bear favorable cytogenetic and/or molecular features, eg, core-binding factor abnormalities, FLT3 Internal Tandem Duplication (FLT3-ITD) negative/NPM1 mutated, biallelic CCAAT/enhancer binding protein alpha (CEBPA) mutation without FLT3-ITD* Chronic myeloid leukemia blast crisis (CML-BC)** Relapsed or refractory to at least one Bcr-Abl-TKI-containing regimen* Myelodysplastic syndrome (MDS), must meet all of the following:** Higher risk MDS [intermediate-2 or high risk by the original International Prognostic Scoring System (IPSS)]** Relapsed, refractory, or intolerant to at least one prior line of therapy containing hypomethylating agents (deoxyribonucleic acid [DNA] methyltransferase inhibitors) No features suggestive of myelodysplastic syndrome (MDS) or acute myelogenous leukemia (AML) on peripheral blood smear or bone marrow biopsy, if clinically indicated Evidence suggestive of myelodysplastic syndrome (MDS) or acute myelogenous leukemia (AML) on peripheral blood smear or bone marrow biopsy, if clinically indicated* No prior allogeneic bone marrow transplant or double umbilical cord blood transplantation (dUBCT) Patients may not have features suggestive of myelodysplastic syndrome (MDS) or acute myelogenous leukemia (AML) on peripheral blood smear or bone marrow biopsy, if clinically indicated No features suggestive of myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) on peripheral blood smear Patients with myelodysplastic syndrome (MDS) or acute myelogenous leukemia (AML), or features suggestive of MDS/AML No features suggestive of myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) on peripheral blood smear Patients with a history of myelodysplastic syndrome (MDS) Participants with myelodysplastic syndrome/acute myeloid leukemia or with features suggestive of myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) Patients with myelodysplastic syndrome/acute myeloid leukemia