This randomized phase I trial is studying the side effects and best dose of two different schedules of sorafenib in treating patients with refractory or relapsed acute leukemia, myelodysplastic syndromes, or blastic phase chronic myelogenous leukemia. Sorafenib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth and by blocking blood flow to the cancer.

PRIMARY OBJECTIVES:

I. Determine the maximum tolerated dose of sorafenib when administered in two different schedules in patients with refractory or relapsed acute leukemia, myelodysplastic syndromes, or blastic phase chronic myelogenous leukemia.

II. Determine the dose-limiting toxicity of this drug in these patients.

SECONDARY OBJECTIVES:

I. Determine the clinical activity of this drug in these patients. II. Determine the biologic effect of this drug in these patients.

OUTLINE: This is a randomized, dose-escalation phase I study. Patients are randomized to 1 of 2 treatment arms.

Arm I: Patients receive oral sorafenib once or twice daily on days 1-5, 8-12, and 15-19.

Arm II: Patients receive oral sorafenib once or twice daily on days 1-14.

In both arms, treatment repeats every 21 days for up to 6 months in the absence of disease progression or unacceptable toxicity. Patients achieving complete remission or partial remission after 6 months may continue therapy at the discretion of the principal investigator.

In both arms, cohorts of 3-6 patients receive escalating doses of sorafenib until the maximum tolerated dose (MTD) is determined. The MTD is defined as the dose preceding that at which 2 of 3 or 2 of 6 patients experience dose-limiting toxicity. Up to 10 patients are treated at the MTD.

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)