Bortezomib, Mitoxantrone, Etoposide, and Cytarabine in Relapsed or Refractory Acute Myeloid Leukemia

Inclusion * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care * Female subject is either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control (ie., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study; female subject is not lactating * Male subject agrees to use an acceptable method for contraception for the duration of the study * Relapsed or refractory AML (excluding acute promyelocytic leukemia), based on World Health Organization Classification; all other subtypes of AML will be eligible; refractory disease will be considered failure to respond to 2 cycles of induction chemotherapy (7+3 and 5+2); any number of relapses will be eligible * No evidence of leptomeningeal disease; a lumbar puncture does not need to be performed unless there is clinical suspicion of leptomeningeal disease * Previous treatment related toxicities must have resolved to Grade 1 (excluding alopecia) * Liver enzymes (AST and ALT) can not be greater than 2.5 times the upper limits of normal (ULN), and total bilirubin =\< 1.5 x ULN within 14 days of enrollment * Renal function: Serum creatinine should be =\< 1.5 x ULN within 14 days of enrollment * No serious or poorly controlled medical conditions that could be exacerbated by treatment or that would seriously complicate compliance with the protocol * ECOG performance status 0-3 * No peripheral neuropathy \>= Grade 2 within 14 days of trial enrollment * Echocardiogram or MUGAs scan demonstrating an ejection fraction \>= 45% * Patients with secondary AML, and patients with a prior autologous and allogeneic bone marrow transplant are eligible * Patients with an allogeneic transplant must meet the following conditions: the transplant must have been performed more than 90 days before registration to this study, the patient must not have \>= Grade 2 acute graft versus host disease (GvHD), or either moderate or severe limited chronic GvHD, or extensive chronic GvHD of any severity; the patient must be off all immunosuppression for at least 2 weeks * No uncontrolled infections * No history of hypersensitivity to boron or mannitol * No known history of HIV or active hepatitis B or C * No major surgery within 4 weeks prior to trial enrollment Exclusion * Myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities; prior to study entry, any ECG abnormality at Screening has to be documented by the investigator as not medically relevant * Patient has \>= Grade 2 peripheral neuropathy within 14 days before enrollment * Female subject is pregnant or breast-feeding; confirmation that the subject is not pregnant must be established by a negative serum beta-human chorionic gonadotropin (beta-hCG) pregnancy test result obtained during screening; pregnancy testing is not required for post-menopausal or surgically sterilized women * Patient has received any standard or investigational therapy for their leukemia within 14 days before enrollment (except for hydrea) * Serious medical or psychiatric illness likely to interfere with participation in this clinical study * Patients with prior malignancy are eligible; however, the patient must be in remission from the prior malignancy and have completed all chemotherapy and radiotherapy at least 6 months prior to registration and all treatment-related toxicities must have resolved * Leptomeningeal/ central nervous system involvement with AML; a lumbar puncture does not need to be performed unless there is clinical suspicion * Patients who have had prior pulmonary radiation * Prohibited Concurrent Therapy: any investigational agent other than VELCADE; G-CSF and GM-CSF are not allowed