Topotecan Hydrochloride and Carboplatin With or Without Veliparib in Treating Advanced Myeloproliferative Disorders and Acute Myeloid Leukemia or Chronic Myelomonocytic Leukemia

Inclusion Criteria:

* PRE-REGISTRATION ELIGIBILITY CRITERIA
* Newly diagnosed acute myeloid leukemia (AML) associated with antecedent myeloproliferative disorder (polycythemia vera, essential thrombocythemia, myelofibrosis, atypical chronic myeloid leukemia, chronic myelomonocytic leukemia and related undifferentiated myeloproliferative/myelodysplastic disorders)
* Relapsed/refractory AML associated with antecedent myeloproliferative disorder (polycythemia vera, essential thrombocythemia, myelofibrosis, atypical chronic myeloid leukemia, chronic myelomonocytic leukemia and related undifferentiated myeloproliferative/myelodysplastic disorders) who have received two or fewer prior induction chemotherapy courses
* Accelerated phase myeloproliferative disorders per Zeider et al with two or fewer prior therapies

  * For aggressive phase myeloproliferative disorders (MPD) (polycythemia vera, essential thrombocythemia, Philadelphia \[Ph\]-negative chronic myelogenous leukemia), one or more of the following criteria must be met: marrow blasts \> 5%, peripheral blood blasts plus progranulocytes \> 10%, new onset or increasing myelofibrosis, new onset or \> 25% increase in hepatomegaly or splenomegaly, new onset constitutional symptoms (fever, weight loss, splenic pain, bone pain). Zeider et al
  * For chronic myelomonocytic leukemia (CMML), the following criteria must be met: 5-19% bone marrow blasts (aggressive) or \>= 20% marrow blasts (transformation)
* Bone marrow and/or peripheral blood specimens will be submitted for correlative studies; patients with a dry tap will still be eligible
* RANDOMIZATION ELIGIBILITY CRITERIA
* Bone marrow aspirate and/or peripheral blood specimens were submitted to the central lab and site has confirmation by the local institution that the patient meets one of the criteria specified above
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 or Karnofsky \>= 60%
* Total bilirubin less than 2.0 mg/dL unless due to Gilbert's syndrome, then less than 5.0 mg/dL
* Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) less than 5 x institutional upper limit of normal
* Creatinine clearance glomerular filtration rate (GFR) greater than 30 ml/min per modified Cockcroft-Gault formula
* Interval of greater than 4 weeks since allogeneic blood or marrow transplantation (BMT) if performed; and absence of active graft versus host disease (GVHD)
* The effects of veliparib on the developing human fetus are unknown; for this reason and because PARP inhibiting agents as well as topoisomerase inhibitors and platinating agents are known to be teratogenic, women of child-bearing potential 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 for 6 months following the last dose of study drug; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of veliparib administration
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Patients who have had chemotherapy or radiotherapy within 4 weeks prior to entering the study with the exception of hydroxyurea for cytoreduction; therapy with tyrosine kinase inhibitors (TKIs) directed against JAK2, BCR-ABL or FLT3 will be allowed to be continued until 24 hours prior to start of therapy on trial
* Patients with active uncontrolled infection; antibiotic therapy for fevers, and continuation of treatment of prior infection are allowed
* Patients who have active central nervous system (CNS) disease are excluded; patients with known active CNS leukemia should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events
* Patients who are receiving any other investigational agents; patients who have completed therapy with an investigational agent should be off this therapy for at least 5 half-lives or two weeks, whichever is shorter
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to veliparib, topotecan or carboplatin
* Uncontrolled intercurrent illness including, but not limited to, 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 are excluded from this study because veliparib is PARP inhibiting agent with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with veliparib, breastfeeding should be discontinued if the mother is treated with veliparib; these potential risks may also apply to topotecan and carboplatin used in this study
* Human immunodeficiency virus (HIV)-patients positive patients are not excluded if they have CD4+ cells \>= 250/mm\^3 and negligible viral load and are on a stable combination antiretroviral therapy
* History of uncontrolled seizure disorder, including focal or generalized seizure within the past year