Brief Summary: RATIONALE: Bortezomib and midostaurin may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as mitoxantrone hydrochloride, etoposide, and cytarabine, work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Giving bortezomib and midostaurin together with combination chemotherapy may kill more cancer cells. PURPOSE: This phase I trial is studying the side effects and best dose of bortezomib when given together with midostaurin with or without combination chemotherapy in treating patients with relapsed or refractory acute myeloid leukemia.

Detailed Description: PRIMARY OBJECTIVES: I. To determine the maximum tolerated dose (MTD) of bortezomib in combination with midostaurin and intensive chemotherapy in patients with relapsed/refractory acute myeloid leukemia (AML). II. To define the specific toxicities and the dose limiting toxicity (DLT) of midostaurin and bortezomib in combination with intensive chemotherapy in relapsed/refractory AML. SECONDARY OBJECTIVES: I. To determine the rate of complete remission (CR) of midostaurin and bortezomib in combination with intensive chemotherapy. II. To determine the overall response rate (ORR). III. To characterize the biological activity of midostaurin and bortezomib to potentially increase endogenous phosphatase activity and therefore inhibit aberrant tyrosine kinases by assessing FLT3 and KIT tyrosine kinase activity as well as SHP-1(Anti-Src Homology Phosphatase-1)phosphatase activity. IV. To correlate the biological activity of midostaurin and bortezomib to potentially increase endogenous phosphatase activity with clinical response. V. To conduct pharmacokinetic studies of midostaurin and bortezomib together and in combination with intensive chemotherapy. VI. To determine the efficacy of midostaurin and bortezomib in combination with intensive chemotherapy at the maximum tolerated dose in patients with FLT3 or KIT tyrosine kinase mutations. OUTLINE: This is a dose escalation study of bortezomib. Patients are assigned to 1 of 2 treatment groups. GROUP I (Dose levels 1-2): Patients receive oral midostaurin twice daily on days 1-14 and bortezomib IV on days 1, 4, 8, and 11. Treatment repeats every 28 days for up to 3 courses in the absence of disease progression or unacceptable toxicity. GROUP II (Dose levels 3-6): Patients receive mitoxantrone hydrochloride IV over 10 minutes, etoposide IV over 1 hour, and cytarabine IV over 6 hours on days 1-6. Patients also receive oral midostaurin twice daily on days 8-21 and bortezomib IV on days 8, 11, 15, and 18. Treatment continues in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up for 30 days.