Sorafenib in Treating Patients With Refractory or Relapsed Acute Leukemia, Myelodysplastic Syndromes, or Blastic Phase Chronic Myelogenous Leukemia

Inclusion Criteria:

Diagnosis of 1 of the following: Acute myeloid leukemia (Acute promyelocytic leukemia (M3) allowed provided patient has failed prior therapy with both tretinoin and arsenic alone or in combination); Acute lymphoblastic leukemia; Myelodysplastic syndromes; Blastic phase chronic myelogenous leukemia (Failed OR intolerant to imatinib mesylate)
Must have failed prior therapy with >= 1 cytotoxic- or biologic-targeted agent (e.g., hypomethylating agents, farnesyl transferase inhibitors, thalidomide, or tyrosine kinase inhibitors); Any number of prior regimens allowed
Performance status: ECOG 0-1
ALT =< 2.5 times upper limit of normal
Bilirubin =< 1.5 mg/dL
Creatinine =< 2.0 mg/dL OR Creatinine clearance >= 60 mL/min
Fertile patients must use effective contraception
No psychiatric illness or social situation that would preclude study compliance
Prior bone marrow transplantation allowed
At least 2 weeks since prior cytotoxic agents OR at least 5 half-lives for non-cytotoxic agents in the absence of rapidly progressing disease
At least 24 hours since prior hydrea for control of peripheral blood leukemia cell counts
Hydroxyurea allowed up to 72 hours after start of therapy with sorafenib
No persistent, chronic, clinically significant toxicities > grade 1 from prior chemotherapy

Exclusion Criteria:

Cytopenias secondary to multilineage bone marrow failure allowed
Ineligible for or not willing to undergo allogeneic stem cell transplantation OR no donor available
Absolute blast count=< 20,000/mm^3 unless patient has documented fms-like tyrosine kinase 3 internal tandem duplication
No evidence of bleeding diathesis (except due to low platelets associated with the primary disease)
No New York Heart Association class III or IV congestive heart failure
No uncontrolled hypertension (i.e., sustained systolic blood pressure [BP] >= 150 mm Hg or diastolic BP >= 90 mm Hg)
No unstable angina pectoris
No symptomatic cardiac arrhythmia requiring and not responding to medical intervention
Not pregnant or nursing
No history of allergic reaction attributed to compounds of similar chemical or biological composition to the study drug
No swallowing dysfunction that would impede oral ingestion of tablets
No active uncontrolled infection
No other uncontrolled illness
No prior sorafenib
No other concurrent investigational or commercial agents, except for standard intrathecal chemotherapy for the treatment of isolated CNS leukemic involvement
No other concurrent anticancer agents
No concurrent combination antiretroviral therapy for HIV-positive patients
No concurrent therapeutic anticoagulation (Concurrent prophylactic anticoagulation [i.e., low-dose warfarin, catheter flushing with heparin] of venous or arterial access devices allowed)
No concurrent cytochrome P450 enzyme-inducing antiepileptic agents, including, but not limited to, any of the following: Phenytoin; Carbamazepine; Phenobarbital; Rifampin
No concurrent Hypericum perforatum (St. John's wort)