This phase I/II trial studies the side effects and best dose of filgrastim (granulocyte colony-stimulating factor [G-CSF]), cladribine, cytarabine, and mitoxantrone, when given together with sorafenib and to see how well they work in treating patients with newly-diagnosed acute myeloid leukemia or high-risk myelodysplastic syndrome (likely to be more aggressive). Drugs used in chemotherapy, such as cladribine, cytarabine, and mitoxantrone work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Colony-stimulating factors, such as filgrastim, may increase the production of blood cells and may help the immune system recover from the side effects of chemotherapy. Sorafenib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Giving filgrastim, cladribine, cytarabine, and mitoxantrone together with sorafenib may kill more cancer cells.

OUTLINE: This is a phase I, dose-escalation study of mitoxantrone and sorafenib followed by a phase II study.

INDUCTION: Patients receive mitoxantrone intravenously (IV) over 60 minutes on days 1-3 and sorafenib orally (PO) twice daily (BID) on days 10-19 in the absence of disease progression or unacceptable toxicity. Patients also receive filgrastim subcutaneously (SC) once daily (QD) on days 0-5, cladribine IV QD over 2 hours on days 1-5, and cytarabine IV QD over 2 hours on days 1-5 in the absence of disease progression or unacceptable toxicity. Patients achieving partial remission (including MRD positive [pos] CR, CR with incomplete platelet recovery [CRp], and CR with incomplete count recovery [CRi]) or persistent AML may receive up to 2 cycles of induction therapy per the discretion of the treating physician.

POST-REMISSION: Patients receive sorafenib PO BID on days 8-27 or 3 days prior to next cycle of treatment, whichever occurs first. Patients also receive filgrastim subcutaneously SC QD on days 0-5, cladribine IV QD over 2 hours on days 1-5, and cytarabine IV QD over 2 hours on days 1-5 in the absence of disease progression or unacceptable toxicity. Patients achieving MRDneg CR may receive up to 4 cycles of post-remission therapy. Patients achieving disease response (MRDpos CR, CRi/CRp, or persistent disease) may receive up to two induction cycles and 1 cycle of post-remission therapy with mitoxantrone omitted in cycle 3. If they then enter MRDneg CR, they can proceed with up to a total of 4 cycles of post-remission therapy.

MAINTENANCE THERAPY: Patients achieving MRDneg CR may receive maintenance therapy of sorafenib PO BID for up to 1 year.

After completion of study treatment, patients are followed up every 3 months for up to 5 years.

Inclusion Criteria:

• Age 18-60 years, inclusive
• Newly diagnosed disease with either a diagnosis of "high-risk" MDS (>= 10% blasts in marrow or blood), high-risk myeloproliferative neoplasm (MPN; >= 10% blasts in blood or bone marrow), or AML other than acute promyelocytic leukemia (APL) with t(15;17)(q22;q12) or variants according to the 2008 World Health Organization (WHO) classification. Patients with biphenotypic AML are eligible; such "high-risk" MDS or MPN have natural history much closer to AML than to lower risk MDS or MPN and have responded similarly to "AML-type" therapy.
• Outside diagnostic material is acceptable as long as peripheral blood and/or bone marrow slides are reviewed at the study institution by appropriate clinical staff. Flow cytometric analysis of peripheral blood and/or bone marrow should be performed according to institutional practice guidelines.
• Treatment-related mortality (TRM) score =< 13.1 as calculated with simplified model
• The use of hydroxyurea prior to study registration is allowed. Patients with symptoms/signs of hyperleukocytosis, white blood cell (WBC) > 100,000/uL, or acute symptoms can be treated with leukapheresis or may receive up to 2 doses of cytarabine (up to 500 mg/m^2/dose) prior to study day 0 enrollment
• Bilirubin =< 2 times institutional upper limit of normal unless elevation is thought to be due to hepatic infiltration by AML, Gilbert's syndrome, or hemolysis (assessed within 10 days prior to study day 0)
• Serum creatinine =< 2.0 mg/dL (assessed within 10 days prior to study day 0)
• Left ventricular ejection fraction >= 45%, assessed within 3 months prior to study day 0, e.g. by multi gated acquisition scan (MUGA) scan or echocardiography, or other appropriate diagnostic modality and no clinical evidence of congestive heart failure
• Women of childbearing potential and men must agree to use adequate contraception beginning at the signing of the consent until at least 3 months after the last dose of study drug
• Provide written informed consent (or legal representative)

Exclusion Criteria:

• Myeloid blast crisis of chronic myeloid leukemia (CML), unless patient is not considered candidate for CML-directed tyrosine kinase inhibitor treatment (excluding sorafenib)
• Concomitant illness associated with a likely survival of < 1 year
• Active systemic fungal, bacterial, viral, or other infection, unless disease is under treatment with anti-microbials and/or controlled or stable (e.g. if specific, effective therapy is not available/feasible or desired [e.g. chronic viral hepatitis, human immunodeficiency virus (HIV)]). Patient needs to be clinically stable as defined as being afebrile and hemodynamically stable for 24-48 hours prior to study day 0, unless fever is thought to be secondary to the underlying hematologic disease.
• Active or clinically significant (or symptomatic) cardiac disease, including active coronary artery disease, cardiac arrhythmias requiring anti-arrhythmic therapy other than beta blockers or digoxin within the last 3 months, unstable angina (anginal symptoms at rest), new-onset angina within 3 months before randomization, or myocardial infarction within 6 months before study day 0
• Previous receipt of azacitidine, decitabine, anthracyclines, cytarabine, or other nucleoside analogues for treatment of AML or MPN/MDS other than as noted for cytarabine
• Pregnancy or lactation
• Concurrent treatment with any other investigational agent that has anti-leukemia activity or another drug with anti-AML-activity