Veliparib and Topotecan With or Without Carboplatin in Treating Patients With Relapsed or Refractory Acute Leukemia, High-Risk Myelodysplasia, or Aggressive Myeloproliferative Disorders

Inclusion Criteria:

* Pathologically confirmed diagnosis of 1 of aggressive MPD or AML out of MPD
* Aggressive phase high-risk myeloproliferative disorders (i.e., polycythemia vera, essential thrombocythemia, or Ph-negative chronic myelogenous leukemia) meeting ≥ 1 of the following criteria:

  * Marrow blasts \> 5%
  * Peripheral blood blasts plus progranulocytes \> 10%
  * New onset or increasing myelofibrosis OR;
* New onset or \> 25% increase in hepatomegaly or splenomegaly
* New onset constitutional symptoms (i.e., fever, weight loss, splenic pain, or bone pain)
* Patients who failed primary induction therapy or relapsed after achieving complete remission are eligible
* No active CNS leukemia; patients with a history of CNS disease must be stable for \> 3 months after treatment and off steroid treatment prior to study enrollment
* Chronic myelomonocytic leukemia meeting either of the following criteria:

  * 5-19% bone marrow blasts (aggressive)
  * At least 20% marrow blasts (transformation)
* ECOG performance status 0-2
* No hyperleukocytosis with \>= 50,000 blasts/uL
* AST, ALT, and alkaline phosphatase =\< 5 times upper limit of normal
* Bilirubin =\< 2.0 mg/dL
* Creatinine normal OR creatinine clearance \>= 60 mL/min
* LVEF \>= 45% by MUGA or ECHO
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception during and for 30 days after completion of study therapy
* No active disseminated intravascular coagulation
* No active uncontrolled infection
* Patients with infection that is under active treatment and controlled with antibiotics are eligible
* No other life-threatening illness
* No mental deficits and/or psychiatric history that would preclude giving informed consent or following protocol
* No prior or current seizure disorder or a history of seizure
* No more than 3 prior cytotoxic regimens
* At least 3 weeks since prior cytotoxic chemotherapy
* At least 2 weeks since prior radiotherapy
* At least 4 weeks since prior autologous or allogeneic stem cell transplantation
* No active graft-versus-host disease
* At least 1 week since prior biologic therapies, including hematopoietic growth factors
* At least 24 hours since prior hydroxyurea, steroids, imatinib mesylate, arsenic trioxide, interferon, or other noncytotoxic agents for blast count control
* No prior ABT-888
* No other concurrent chemotherapy, radiotherapy, or immunotherapy
* No concurrent antiretroviral therapy for HIV-positive patients
* No other concurrent investigational or commercial agents or therapies for this cancer