Bortezomib and Vorinostat in Younger Patients With Refractory or Relapsed MLL Rearranged Hematologic Malignancies

INCLUSION CRITERIA: * Age: Patient is ≤ 21 years of age (i.e., eligible until 22nd birthday). * Diagnosis: Participant has a hematologic malignancy that is positive for MLLr as determined by fluorescent in situ hybridization (FISH) or RT-PCR, and disease meets at least one of the following criteria: * Relapsed after or is refractory to chemotherapy * Relapsed after hematopoietic stem cell transplantation (HSCT) * Relapsed or refractory secondary leukemia (Relapse is defined as reappearance of leukemia cells after the attainment of complete remission and refractory is defined as ≥5% blasts at the end of induction. Patients that achieved MRD negative status followed by reappearance of blasts at less than 5% are eligible.) * Patients must have had verification of the malignancy at relapse, including immunophenotyping, to confirm diagnosis. * Performance Level: Karnofsky ≥50% for patients \>16 years of age and Lansky ≥50 for patients ≤16 years of age (See Appendix III). Patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score. * Prior therapy: * Patients who relapse while receiving standard ALL maintenance chemotherapy consisting of daily 6MP, weekly methotrexate, monthly vincristine, and monthly steroid pulse will not be required to have a waiting period before entry onto this study. * Patients who relapse on therapy other than standard ALL maintenance therapy must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study. * Cytotoxic therapy: At least 14 days since the completion of cytotoxic therapy with the exception of hydroxyurea, low dose cytarabine, and intrathecal chemotherapy which is permitted up to 24 hours prior to the start of protocol therapy. For patients with aggressive disease that is in the peripheral blood and rising, this 14 day washout period may be omitted. * Biologic (anti-neoplastic) agent: At least 7 days since the completion of therapy with a biologic agent or donor lymphocyte infusions (DLI). For agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur. * Stem cell transplant or rescue: ≥2 months must have elapsed since the time of transplant. Patients with active graft-vs-host disease (GVHD) are not eligible. * Organ function requirements: All patients must have: * Adequate renal function defined as: Creatinine clearance or radioisotope GFR ≥70 mL/min/1.73 m\^2, OR adequate serum creatinine based on age/gender. * Adequate liver function defined as: Total bilirubin ≤ ULN for age, or if total bilirubin is \> ULN, direct bilirubin is ≤ 1.4 mg/dL, AND SGPT (ALT) ≤4 x ULN for age, unless elevation due to leukemic infiltration * Adequate cardiac function defined as: Shortening fraction of ≥27% by echocardiogram OR Ejection fraction of ≥50% by gated radionuclide study * Central nervous system (CNS) function defined as: Patients with seizure disorder may be enrolled if on allowed anti-convulsants and well controlled. Benzodiazepines and gabapentin are acceptable. CNS toxicity ≤ Grade 2. * Adequate pulmonary function defined as FVC\>50% predicted OR, if unable to perform pulmonary function testing, must maintain pulse oximetry oxygen saturation \>92% on room air. EXCLUSION CRITERIA: * Patients requiring anticonvulsants known to activate the cytochrome p450 system, in particular anticonvulsants such as phenytoin, carbamazepine, and phenobarbital, are not eligible. Benzodiazepines and gabapentin are acceptable. Please see Appendix I for a list of drugs known to be potent inducers/inhibitors of the cytochrome p450 system and Appendix II for a list of anticonvulsants based on CYP3A4/5 enzyme induction. * ALL patients who cannot receive any asparaginase products (E. Coli, PEG-asparaginase, or Erwinia asparaginase) on this study (eg, due to prior severe pancreatitis, stroke or other toxicity) are not eligible. Patients with clinically significant prior allergies to PEG-asparaginase are eligible if Erwinia L-asparaginase can be substituted. * Pregnancy and breast feeding: patients who are pregnant or breast-feeding are not eligible for this study as there is as yet no available information regarding human fetal or teratogenic toxicities. Negative pregnancy tests must be obtained in girls who are post-menarchal. Males or females of reproductive potential may not participate unless they have agreed to use an effective birth control method. * Investigational drugs: Patients who are currently receiving another investigational drug are not eligible. * Anti-cancer agents: Patients who are currently receiving other anti-cancer agents with the exception of those delineated in the eligibility criteria. * Infection: Patients who have an uncontrolled infection are not eligible. Infections controlled on concurrent anti-microbial agents are acceptable, and anti-microbial prophylaxis per institutional guidelines are acceptable. * Known human immunodeficiency virus (HIV) infection (pre-study testing not required). * Any significant concurrent disease, illness, or psychiatric disorder that would compromise patient safety or compliance, study participation, follow up, or interpretation of study research. * Patients with Fanconi anemia, Kostmann syndrome, Shwachman syndrome, or other inherited bone marrow failure syndromes are not eligible. * Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible.