A diagnosis of acute promyelocytic leukemia (APL) or chronic myeloid leukemia (CML) in blast crisis. Subject has BCR-ABL-positive leukemia (Chronic myeloid leukemia [CML] in blast crisis). Patients with myeloid diseases (AML, myeloid blast crisis of CML) will be eligible for arm A with cytarabine; patients with lymphoid diseases (ALL, lymphoid blast crisis of CML) will be eligible for arm B with liposomal vincristine; patients with leukemia of ambiguous lineage or bi-phenotypic leukemia (e.g. B/myeloid) may be treated on either arm A or B, at discretion of treating physician Myeloid blast crisis of chronic myeloid leukemia (CML), unless patient is not considered candidate for tyrosine kinase inhibitor treatment CML in blast crisis Myeloid blast crisis of chronic myeloid leukemia (CML), unless patient is not considered candidate for tyrosine kinase inhibitor treatment Myeloid blast crisis of chronic myeloid leukemia (CML), unless patient is not considered candidate for CML-directed tyrosine kinase inhibitor treatment (excluding sorafenib) CML in blast crisis Chronic myeloid leukemia (CML) in refractory blast crisis Patients who are in blast transformation of chronic myeloid leukemia (CML); prior MDS or CMML is acceptable Newly diagnosed or relapsed chronic myelogenous leukemia (CML) in lymphoid blast crisis Chronic myelogenous leukemia (CML) in second chronic phase after accelerated or blast crisis; blast crisis defined as:\r\n* Blast count >= 20% in the peripheral blood or bone marrow\r\n* Large foci of blasts on bone marrow\r\n* Presence of extra-medullary blastic infiltrate (myeloid sarcoma or chloroma) Chronic myeloid leukemia (CML) which:\r\n* Failed to achieve a cytogenetic remission to tyrosine kinase inhibitor treatment or has a cytogenetic relapse\r\n* Has ever been in accelerated phase or blast crisis Chronic myelogenous leukemia (CML) in refractory blast crisis CML in blast crisis Myeloid blast crisis of chronic myeloid leukemia (CML), unless patient is not considered candidate for tyrosine kinase inhibitor treatment BCR-ABL1 chronic myeloid leukemia in blast crisis (CML-BC) Chronic myelogenous leukemia (CML) in refractory blast crisis Patients who are in the blast phase of chronic myeloid leukemia Myeloid blast crisis of chronic myeloid leukemia (CML), unless patient is not considered candidate for tyrosine kinase inhibitor treatment Previous diagnosis of accelerated phase or blast crisis Blast phase CML Prior imatinib failure or had accelerated phase or blast crisis CML Patients with APL (FAB type M3) or CML in blast crisis. Refractory/relapsing blast crisis of chronic myelogenous leukemia (CML) Refractory/relapsing myeloid blast crisis of chronic myeloid leukemia (CML), unless patient is not considered candidate for tyrosine kinase inhibitor treatment Relapsed AML, ALL, CML in blast crisis, or MDS Chronic myelogenous leukemia (CML) in blast crisis Previous diagnosis of CML accelerated phase or blast crisis The patient has lymphoid Ph+ blast crisis or blast phase CML. Inclusion Criteria:\n\n For CML patients either:\n\n - a. Patients with Ph+ CML in chronic or accelerated phase who were previously treated\n with at least two different tyrosine kinase inhibitors prior to study entry and are\n relapsed, refractory to or intolerant of TKIs as determined by investigators or\n\n - b. Patients with CML in chronic or accelerated phase who exhibit relapsed disease\n associated with the presence of the T315I \gatekeeper mutation\ after at least one TKI\n are also eligible provided that no other effective therapy exists\n\n For ALL and CML-BP patients:\n\n - Patients with CML BP or Ph+ ALL who have a cytopathologically confirmed diagnosis and\n are relapsed or refractory to at least one prior TKI or intolerant of TKIs. TKI\n failure for Ph+ ALL and CML-BP patients is defined as at least the loss of Molecular\n Response (MR) 4.5 (BCR-ABL ? 0.0032%)\n\n - Eastern Cooperative Oncology Group (ECOG) performance status 0 to 2\n\n - Willingness and ability to comply with all study procedures\n\n - Written informed consent obtained prior to any screening procedures\n\n Exclusion Criteria:\n\n Wash-out period:\n\n - Systemic antineoplastic therapy (including cytotoxic chemotherapy, alfa-interferon and\n toxin immunoconjugates) or any experimental therapy within 14 days or 5 half-lives,\n whichever is shorter, before the first dose of study treatment\n\n - Therapy with TKIs as single agent within 5 half-lives before the first dose of study\n treatment\n\n - Unconjugated monoclonal antibody therapies within 28 days or 5 half-lives, whichever\n is shorter, before the first dose of study treatment\n\n - For patients receiving ABL001 in combination with either nilotinib or imatinib or\n dasatinib, intolerance to nilotinib, imatinib or dasatinib, respectivelyRadiotherapy\n with a wide field of radiation within 4 weeks or radiotherapy with a limited field of\n radiation for palliation within 1 week of the first dose of study treatment.\n\n - CNS irradiation for meningeal leukemia, except if radiotherapy occurred > 3 months\n previously. At least four weeks must have elapsed since prophylactic CNS irradiation\n given as part of a front-line therapy regimen for ALL\n\n - Major surgery within 2 weeks before the first dose of study treatment\n\n Other protocol-defined inclusion/exclusion criteria may apply Chronic myeloid leukemia (CML): patients in chronic phase 1 (CP1) must have failed or be intolerant of tyrosine kinase inhibitors (TKIs); patients beyond CP1 will be accepted if they have < 5% marrow blasts at time of transplant Chronic Myelogenous Leukemia (CML) in first or subsequent chronic phase failing to respond (or intolerant) to at least two different tyrosine kinase inhibitors. CML in accelerated or blast phase (CML-AP/BP) are eligible without requirement to fail tyrosine kinase inhibitor therapy, but must be in remission at time of enrollment. Remission is defined as the absence of blasts in the peripheral circulation at the time of enrollment, < 5% blasts in the bone marrow and absence of extramedullary disease including CNS involvement. Subjects diagnosed with Ph+ CML-CP, Ph+ CML-AP, Ph+ CML-BP, or Ph+ ALL Chronic myeloid leukemia (CML) – patients in CP1 must have failed or be intolerant of tyrosine kinase inhibitors (TKIs); patients beyond CP1 will be accepted if they have < 5% marrow blasts at time of transplant Chronic myelogenous leukemia in chronic or accelerated phase; chronic phase patients must failed at least two different TKIs, been intolerant to all available TKIs or have T315I mutation Chronic myeloid leukemia (CML) >= 1st chronic phase, after failed >=2 lines of tyrosine kinase inhibitors; patients who progressed to blast phase must be in morphologic remission at transplant Histologically documented diagnosis of Ph+ CML, in accelerated or blast phase. One of the following parameters is required to meet criteria for accelerated CML: Chronic myeloid leukemia (CML) who have failed or are intolerant to BCR-ABL tyrosine kinase inhibitors CML with accelerated or blast phase with < 20% blasts after therapy Chronic myeloid leukemia (CML) in any phase CML in any phase Chronic myeloid leukemia (CML) second chronic phase or accelerated phase Newly diagnosed, previously untreated chronic phase chronic myeloid leukemia (CP-CML) (by World Health Organization [WHO] definition) (hydroxyurea permitted up to 7 days prior to enrollment) Chronic myeloid leukemia (CML) in AP or BP Patients in late chronic phase (i.e., time from diagnosis to treatment > 12 months), accelerated or blast phase are excluded; the definitions of CML phases are as follows: \r\n* Early chronic phase: \r\n** Time from diagnosis to therapy 12 months\r\n** Late chronic phase: \r\n*** Time from diagnosis to therapy > 12 months\r\n* Blastic phase: \r\n** Presence of 30% blasts or more in the peripheral blood or bone marrow\r\n* Accelerated phase CML: \r\n** Presence of any of the following features: \r\n*** Peripheral or marrow blasts 15% or more\r\n*** Peripheral or marrow basophils 20% or more\r\n*** Thrombocytopenia < 100 x 109/L unrelated to therapy\r\n*** Documented extramedullary blastic disease outside liver or spleen Have Chronic Phase Chronic Myeloid Leukemia (CP-CML) and have received at least two prior tyrosine-kinase inhibitor (TKI) therapies and have demonstrated resistance to treatment OR have documented history of presence of T3151 mutation after receiving any number of prior TKI a. The diagnosis of CML will be made using standard hematopathologic and cytogenetic criteria; CP-CML will be defined by all of the following: i) < 15% blasts in bone marrow ii) < 30% blasts plus promyelocytes in bone marrow iii) < 20% basophils in peripheral blood iv) ? 100 × 109/L platelets (? 100,000/mm^3) v) No evidence of extramedullary disease except hepatosplenomegaly vi) No prior diagnosis of accelerated phase (AP-CML), and blastic phase (BP-CML) b. Cytogenetic assessment at screening must demonstrate the BCR-ABL1 fusion by presence of the t(9;22) Philadelphia chromosome i) Variant translocations are only allowed provided they are assessable for cytogenetic response utilizing conventional cytogenetic techniques c. Resistance to prior TKI therapy is defined as follows (participants must meet at least 1 criterion): i) Three months after the initiation of prior TKI therapy: No cytogenetic response (> 95% Ph+) or failure to achieve complete hematologic response (CHR) or new mutation ii) Six months after the initiation of prior TKI therapy: BCR-ABL1IS >10% and/or Ph+ >65% or new mutation iii) Twelve months after the initiation of prior TKI therapy: BCR ABL1IS >10% and/or Ph+ >35% or new mutation. iv) At any time after the initiation of prior TKI therapy, the development of a new BCR-ABL1 kinase domain mutation(s). v) At any time after the initiation of prior TKI therapy, the development of new clonal evolution vi) At any time after the initiation of prior TKI therapy, the loss of CHR, or complete cytogenic response (CCyR), or the confirmed loss of molecular response rate (MRR) in 2 consecutive tests, one of which has a BCR-ABL1IS transcript level of ?1% or new mutation d. > 1% of BCR-ABL1IS as shown by real-time polymerase chain reaction Chronic myelogenous leukemia\r\n* Chronic phase chronic myelogenous leukemia (CML) having progressed after treatment with breakpoint cluster region (BCR)-ABL proto-oncogene 1, non-receptor tyrosine kinase (ABL) kinase inhibitor or with evidence of T315I BCR-ABL mutation\r\n* Accelerated or blast phase CML\r\n* Not eligible for myeloablative allogeneic HSCT RESEARCH PHASE INCLUSION CRITERIA: The malignancy must be restaged prior to research phase and must not have progressed during induction chemotherapy (stable disease or better); persons with acute leukemia, MDS/RAEB-I or -II or CML with previous accelerated or blast phase must have < 5% blasts in the bone marrow; persons with chronic phase CML may have up to 10% blasts in the bone marrow Relapsed or refractory B-cell ALL or CML in lymphoid blast phase; Philadelphia chromosome must be present at screening (as determined by cytogenetic analysis, fluorescence in situ hybridization [FISH], or polymerase chain reaction [PCR] [i.e., BCR-ABL positive]); Note: patients with CML who have received treatment with tyrosine kinase inhibitors for their CML, and have progressed to lymphoid blast phase are eligible for frontline treatment; Frontline Ph+ ALL or CML-lymphoid blast phase (LBC) Cohort: Patients with newly-diagnosed Ph+ ALL or CML-LBC, who have received no or minimal treatment (minimal treatment is defined as treatment with steroids/hydroxyurea of =< 2 week duration; vincristine =< 2 doses; tyrosine kinase inhibitor of =< 4 week duration; =< 2 doses of cytarabine) and are >= 60 years or older are eligible; patients must have bone marrow blasts > 5% at the time of screening Chronic myeloid leukemia (CML): a. failed to achieve cytogenetic remission or have cytogenetic relapse after treatment with at least 2 tyrosine kinase inhibitors, or b. accelerated phase or blast phase at any time Chronic myelogenous leukemia (CML) failing to respond to or not tolerating imatinib, dasatinib, or nilotinib in first chronic phase of disease; or CML in accelerated phase or second chronic phase Interferon- or imatinib-refractory chronic myelogenous leukemia (CML) in first chronic phase, or non-blast crisis CML beyond first chronic phase Chronic myelogenous leukemia (CML) failing to respond to or not tolerating Imatinib or dasatinib in first chronic phase of disease; CML in accelerated phase, second chronic phase, or in CR after accelerated phase or blast crisis MRD positive leukemia (AML, ALL or accelerated/blast phase chronic myeloid leukemia [CML]); selected patients in morphologic CR, but with positive immunophenotypic (flow cytometry) or molecular evidence of MRD may be eligible if recent chemotherapy has not resulted in MRD negative status Chronic myeloid leukemia (CML) second chronic phase or accelerated phase PREREGISTRATION (STEP 0): Patient has pathologically-confirmed chronic phase-CML on a first line TKI and must meet the following criteria:\r\n* This diagnosis of chronic phase-CML must be confirmed by a bone marrow aspirate and/or biopsy with =< 10 % myeloid blasts within two weeks prior to registration; patients with diagnoses of accelerated or blast phase CML are not eligible\r\n* The patient has to be on first-line TKI therapy (the same TKI) for at least 2 years prior to pre-registration\r\n** Dasatinib: 50 – 180 mg per day\r\n** Imatinib: 200 – 800 mg per day\r\n** Nilotinib: 300 – 400 mg every 12-24 hours\r\n* Has been in MMR (i.e. MR^3) but still have detectable BCR-ABL transcript by a standard real-time quantitative polymerase chain reaction (RQ-PCR) assay with a limit of detection (sensitivity) of 4.5 for at least 12 months from the first documentation of the MMR\r\n* Patient has not achieved MR^4.5 (complete molecular remission [CMR]) within the time of initiation of TKI therapy and pre-registration Patients must have chronic phase chronic myeloid leukemia (CML); they must also be under treatment with nilotinib as either first, second or third-line therapy Patients who are in accelerated phase or blast phase CML Chronic myelogenous leukemia (CML)\r\n* Chronic phase CML, refractory to imatinib treatment\r\n* Accelerated phase CML Atypical chronic myeloid leukemia (CML): Philadelphia chromosome-negative patients with a diagnosis of atypical CML Newly diagnosed and untreated Ph+ CML CP or Ph+ CML CP or AP resistant or intolerant to either imatinib or dasatinib Chronic Phase (CP)-CML Ph+ patients with complete hematologic response (CHR) but with one log BCR-ABL reduction (BCR-ABL level >10% IS) 3 months of imatinib 400mg treatment. (Imatinib transient dose adjustments due to Adverse Event (AEs) are allowed with a maximum of 2 weeks interruption of treatment with imatinib (cumulative) within the 3 month period before randomization). Imatinib monotherapy must have been started within 6 months of CP-CML diagnosis (Ph + /BCR-ABL detection) Chronic myeloid leukemia (CML) in 1st or subsequent chronic phase characterized by <10% blasts in the blood or bone marrow. Chronic phase disease is defined as:\r\n* < 15% blasts in peripheral blood and bone marrow; \r\n* < 30% blasts plus promyelocytes in peripheral blood and bone marrow;\r\n* < 20% basophils in peripheral blood; \r\n* >= 100 x 10^9/L platelets (>= 100,000/mm^3); \r\n* No evidence of extramedullary disease except hepatosplenomegaly; and \r\n* No prior diagnosis of accelerated phase (AP) or blastic phase-chronic myeloid leukemia (BP-CML); patients with clonal evolution but no other criteria for accelerated phase are eligible Diagnosed with CML in chronic phase and have either the b3a2 (e14a2) or b2a2 (e13a2) variants that give rise to the p210 BCR-ABL protein Confirmed diagnosis of Chronic Myeloid Leukemia in Chronic Phase or Accelerated Phase : Diagnosis of CML Patient with diagnosis of BCR-ABL positive CML CP Patients must have CML in any phase (CP, AP, or BP of any phenotype) or Ph+ ALL For CML chronic phase (CP) and accelerated phase (AP) patients, received hydroxyurea or anagrelide within 24 hours prior to receiving the first dose of ponatinib; interferon, cytarabine, or immunotherapy within 14 days prior to first dose of ponatinib; or any other cytotoxic chemotherapy, radiotherapy, or investigational therapy within 28 days prior to receiving the first dose of ponatinib. For CML blast phase (BP) patients, received chemotherapy within 14 days prior to the first dose of ponatinib. CML CP patients are excluded if they are in Complete cytogenetic response (CCyR) Patients with CML AP, CML BP, or Ph+ ALL are excluded if they are in Major Hematologic Response (MaHR). A diagnosis of refractory or relapsed AML, or Ph+ CML (in chronic, accelerated or blast phase, or acute lymphoblastic leukemia, or myelodysplastic syndrome. One of the following parameters is required to meet criteria for accelerated phase CML: Chronic myelogenous leukemia (CML): second chronic phase, accelerated phase or blast crises with less than 10% blasts in the bone marrow, or CR1 and resistance to Gleevec or other tyrosine kinase inhibitors Chronic myeloid leukemia (CML) accepted if they are beyond chronic phase (CP)1 and if they have received previous myelosuppressive chemotherapy or HCT and have < 5% marrow blasts at time of transplant CP-CML who prove resistant or intolerant to imatinib (Cohort 1) Ph+ ALL, AP-CML, or BP-CML who are resistant or intolerant to or who relapse after imatinib therapy (Cohort 2) Chronic myelogenous leukemia (CML)\r\n* Chronic phase CML \r\n* Accelerated phase CML\r\n* Not eligible for myeloablative allogeneic HSCT Chronic myelogenous leukemia (CML) second chronic phase or accelerated phase; or Any phase of CML other than chronic phase Diagnosis of Ph-positive or Bcr-positive CML in early chronic phase CML (i.e., time from diagnosis 12 months); except for hydroxyurea, patients must have received no or minimal prior therapy, defined as < 1 month (30 days) of prior interferon-alpha (with or without cytarabine) and/or an Food and Drug Administration (FDA)-approved tyrosine kinase inhibitor (TKI); patients with de novo accelerated phase will be treated but analyzed separately Patients in late chronic phase (i.e., time from diagnosis to treatment > 12 months) or blastic phase are excluded; the definitions of CML phases are as follows: \r\n* Early chronic phase: time from diagnosis to therapy < 12 months; late chronic phase: time from diagnosis to therapy > 12 months\r\n* Blastic phase: presence of 30% blasts or more in the peripheral blood or bone marrow\r\n* Accelerated phase CML: presence of any of the following features:\r\n** Peripheral or marrow blasts 15% or more\r\n** Peripheral or marrow basophils 20% or more\r\n** Thrombocytopenia < 100 x 10^9/L unrelated to therapy\r\n** Documented extramedullary blastic disease outside liver or spleen due to past causes\r\n* Clonal evolution defined as the presence of additional chromosomal abnormalities other than the Ph chromosome is part of accelerated phase CML; Ph chromosome variants or complex Ph chromosome translocations are not considered to indicate disease acceleration; these patients, like others with de novo accelerated phase, will be eligible, and analyzed separately Chronic myeloid leukemia (CML) failing to respond to, progressing on or not tolerating appropriate tyrosine kinase inhibitor (TKI) therapy in first chronic phase of disease; CML in accelerated phase, second chronic phase, or in complete remission (CR) after accelerated phase or blast crisis Patients with advanced CML (CML-AP, CML-BP and Philadelphia chromosome-positive acute leukemia) or refractory chronic phase CML are eligible, as defined as follows: the phase I portion of the study will be conducted first in advanced phase (accelerated phase CML, blast phase CML or Philadelphia-positive acute leukemia) patients; once MTD is identified, a cohort of 6 patients with CML chronic phase who have failed prior therapy with at least two tyrosine kinase inhibitor will be treated at the MTD to determine if this dose is also acceptable for chronic phase patients; the phase II will be conducted in two treatment arms as follows: treatment Arm A (advanced phase disease) and treatment Arm B (therapy for chronic phase [CP]-CML refractory/resistant/suboptimally responding to at least two prior tyrosine kinase inhibitors [TKIs]); CML-AP is defined by the presence of one of the following: a. 15-29% blasts in peripheral blood (PB) or bone marrow (BM), b. > 20% basophils in PB or BM, c. > 30% blasts plus promyelocytes (with blasts < 30%) in PB or BM, d. < 100 x 10^9/L platelets unrelated to therapy, or clonal cytogenetics evolution (i.e., the presence of cytogenetic abnormalities other than the Philadelphia chromosome) except if only present at the time of diagnosis and not associated with other features of accelerated phase; CML-BP is defined by the presence of >= 30% blasts in the bone marrow and/or peripheral blood or the presence of extramedullary disease, with myeloid or lymphoid blast morphology; Philadelphia-chromosome acute leukemias are eligible and defined by >= 20% blasts in the peripheral blood or bone marrow at the time of diagnosis Philadelphia positive Chronic Myeloid Leukemia (CML) in chronic phase Previously untreated chronic phase CML, except for Anagrelide or Hydroxyurea. Interferon- or imatinib-refractory chronic myelogenous leukemia (CML) in first chronic phase, or CML in second or subsequent chronic phase Must have one of the following: newly diagnosed CP Ph+CML, CP or AP resistant/ intolerant to imatinib and/or dasatinib, or Ph+ ALL either relapsed after or refractory to standard therapy Chronic myeloid leukemia (CML) >= 1st chronic phase, after failed >= 2 lines of tyrosine kinase inhibitors; in accelerated or blast phase with > 30% bone marrow blasts PATIENTS: Refractory or recurrent hematologic malignancy (lymphoma, leukemia, or myeloma, amyloidosis and chronic myelogenous leukemia [CML] - CML can only be accelerated or blast phase). PATIENTS: Chronic myeloid leukemia (CML) except accelerated or blast phase. Interferon? or tyrosine kinase?refractory chronic myelogenous leukemia (CML) in first chronic phase, tyrosine kinase inhibitor (TKI)?intolerant CML in first chronic phase, or CML in second or subsequent chronic phase CML patients in chronic phase receiving treatment with any Food and Drug Administration (FDA) approved TKI; or CML patients in accelerated or blastic phase who are considered to be in this phase because of thrombocytopenia or because of clonal evolution and with no other criteria for accelerated/blastic phase or patients with myelofibrosis receiving treatment with FDA approved TKI and with peripheral blood and/or bone marrow blasts =< 10% CML patients in accelerated or blastic phase except for those who are considered to be in this phase because of thrombocytopenia or because of clonal evolution and with no other criteria for accelerated/blastic phase; or myelofibrosis patients who have transformed to acute leukemia or have >= 10% blasts in peripheral blood and/or in bone marrow Myelodysplasia (MDS) and chronic myeloid leukemia (CML): must have < 5% marrow blasts Chronic myelogenous leukemia (CML) with one of the following criteria:\r\n* Accelerated phase, defined by any of the following:\r\n** Blasts 10-19% in peripheral blood white cells or bone marrow \r\n** Peripheral blood basophils at least 20%\r\n** Persistent thrombocytopenia (< 100 x 10^9/l) unrelated to therapy, or persistent thrombocytosis (> 1000 x 10^9/l) unresponsive to therapy \r\n** Increasing spleen size and increasing white blood cell (WBC) count unresponsive to therapy\r\n** Cytogenetic evidence of clonal evolution (i.e., the appearance of an additional genetic abnormality that was not present in the initial specimen at the time of diagnosis of chronic phase)\r\n* Chronic phase provided a complete hematologic remission was not achieved by 3 months or a complete cytogenetic remission by 18 months and the patient had received at least 2 tyrosine kinase inhibitors Chronic myeloid leukemia (CML) – Patients will be accepted if they have shown intolerance to tyrosine kinase inhibitors or are beyond first chronic phase (CP1) and if they have received previous myelosuppressive chemotherapy or HCT, and have < 5% marrow blasts at time of transplant Patients with a history of non-compliance to CML treatment and monitoring requirements Minimum of 2 calendar years of nilotinib treatment with at least the last 12 months of nilotinib treatment prior to pre-screening at approved total dialy dose of 600 mg BID or at a reduced dose of 400 mg QD if required from the perspective of tolerance for BCR-ABL positive CML in documented chronic phase at the time of diagnosis Previous anticancer agents for CML other than nilotinib except for cytoreduction after CML diagnosis until up to 4 weeks after first dose of nilotinib Known second chronic phase of CML after previous progression to AP/BC In patients with rapidly proliferating disease, hydroxyurea may be administered before study entry, if clinically indicated, to control disease. In such cases, complete hematologic response (CHR) must be sustained for at least 4 weeks for accelerated CML, and at least 8 weeks for chronic phase CML, following the discontinuation of hydroxyurea, to be considered as a CHR. Lymphoid blastic crisis of chronic myelogenous leukemia Chronic myelogenous leukemia excluding refractory blast crisis; to be eligible in first chronic phase (CP1) patient must have failed or be intolerant to imatinib mesylate Diagnosis of Burkitt's leukemia/lymphoma according to WHO classification or chronic myelogenous leukemia lymphoid blast crisis Chronic myelogenous leukemia in chronic or accelerated phase, or chronic myelogenous leukemia (CML) blast crisis in morphological remission (< 5% blasts): chronic phase patients must have failed at least two tyrosine kinase inhibitors been intolerant to all available tyrosine kinase inhibitors (TKIs) or have T315I mutation Chronic myelogenous leukemia excluding refractory blast crisis: To be eligible in first chronic phase (CP1) patient must have failed or be intolerant to imatinib mesylate BCR-ABL-positive leukemia (chronic myelogenous leukemia in blast crisis). Chronic myelogenous leukemia: All types, except refractory blast crisis; chronic phase patients must have failed or been intolerant to Gleevec or other tyrosine kinase inhibitors Chronic myelogenous leukemia: All types, except refractory blast crisis; chronic phase patients must have failed or been intolerant to Gleevec or other tyrosine kinase inhibitors; at time of transplant, patients must have < 5% blasts in an evaluable marrow (> 25% of normal cellularity for age) by morphology within the bone marrow Chronic myelogenous leukemia excluding refractory blast crisis; to be eligible in first chronic phase (CP1) patient must have failed or be intolerant to imatinib mesylate Chronic myelogenous leukemia: all types except refractory blast crisis; chronic phase patients must have failed or been intolerant to Gleevec Chronic myelogenous leukemia excluding refractory blast crisis: to be eligible in first chronic phase (CP1) patient must have failed or be intolerant to one or more tyrosine kinase inhibitors Diagnosis of chronic myelogenous leukemia in blast crisis; Diagnosis of mature B-cell ALL (Burkitt’s leukemia) according to World Health Organization (WHO) classification, or lymphoid blast crisis of chronic myelogenous leukemia (CML) Chronic myelogenous leukemia all types except blast crisis (note treated blast crisis in chronic phase is eligible) Subject has BCR-ABL-positive leukemia (chronic myelogenous leukemia in blast crisis). Diagnosis of Burkitt's Leukemia, or lymphoid blast crisis of chronic myelogenous leukemia (CML) Subject has BCR-ABL-positive leukemia (chronic myelogenous leukemia in blast crisis). Diagnosis of Burkitt's leukemia/lymphoma according to WHO classification or chronic myelogenous leukemia lymphoid blast crisis Subject has BCR-ABL-positive leukemia (chronic myelogenous leukemia in blast crisis). Patients with chronic myelogenous leukemia (CML) in myeloid blast crisis are eligible if their disease has failed to respond, and/or they are intolerant, to the available tyrosine kinase inhibitors (TKIs) Chronic myelogenous leukemia excluding refractory blast crisis; to be eligible in first chronic phase (CP1) patient must have failed or be intolerant to tyrosine kinase inhibitor therapy Burkitt's lymphoma/leukemia or chronic myelogenous leukemia lymphoid blast crisis (p210 BCR-ABL+) Subject has BCR-ABL-positive leukemia (chronic myelogenous leukemia in blast crisis). Diagnosis of chronic myelogenous leukemia in blast crisis Chronic myelogenous leukemia: all types except refractory blast crisis; chronic phase patients must have failed or been intolerant to at least one tyrosine-kinase inhibitor Chronic myelogenous leukemia: all types except refractory blast crisis; chronic phase patients must have failed at least two different tyrosine-kinase inhibitors (TKIs), or been intolerant to all available TKIs or have T315I mutation Known history of chronic myelogenous leukemia (CML) Pathologic confirmation of the diagnosis of AML, ALL (acute lymphoblastic leukemia), or blast-phase CML (chronic myelogenous leukemia) Acute myelogenous leukemia (AML): Patients with mature B-cell ALL or acute myelogenous leukemia (AML) Patients with acute myelogenous leukemia (AML) who are in first or second complete remission MRD positive leukemia (AML, ALL or accelerated/blast phase chronic myelogenous leukemia [CML]); selected patients in morphologic CR, but with positive immunophenotypic (flow cytometry) or molecular evidence of MRD may be eligible if recent chemotherapy has not resulted in MRD negative status Chronic myelogenous leukemia (CML) Patients with a myeloid hematologic malignancy (acute myelogenous leukemia, secondary myelogenous leukemia or myelodysplastic syndrome) unlikely to be cure by standard chemotherapy; this includes patients who have relapsed after standard chemotherapy treatments and patients in first remission with unfavorable prognostics features Chronic myelogenous leukemia (CML) patients who have failed or are intolerant of tyrosine kinase inhibitors or patients with other myeloproliferative diseases who are high risk and the intent of therapy is cure Chronic myelogenous leukemia (CML) in chronic or accelerated phase; prior therapies allowed Chronic myelogenous leukemia in chronic or accelerated phase Chronic myelogenous leukemia (CML) Patients must not have blastic transformation of chronic myelogenous leukemia Patients must have an initial diagnosis of AML, biphenotypic acute leukemia, or APL or chronic myelogenous leukemia (CML) in blast crisis Chronic myelogenous leukemia (accelerated, blast or second chronic phase) Relapse after previous allogeneic stem cell transplant for one of the following hematologic malignancies - acute myelogenous leukemia, acute lymphoblastic leukemia, myelodysplastic syndromes (MDS), lymphoma, myeloma, chronic lymphocytic leukemia, chronic myelogenous leukemia meeting the following:\r\n* For non-chronic myelogenous leukemia (CML), relapse will be defined based on disease specific morphologic criteria from a bone marrow biopsy and aspirate or recurrence of disease specific cytogenetics; relapse can be determined morphologically; equivocal results for relapse should result in a repeated test after an appropriate time interval (suggested 1 month) to determine eligibility\r\n* For CML, relapse will be defined as any cytogenetic evidence of a Philadelphia chromosome or persistence of breakpoint cluster region (BCR)/c-abl oncogene 1, non-receptor tyrosine kinase (ABL) rearrangements by molecular testing on at least two measurements over a 6 month interval; if cytogenetics are normal and there is polymerase chain reaction (PCR) evidence of a BCR/ABL fusion, patients will be eligible if they have evidence of a quantitative increase in CML measured either by quantitative PCR or by fluorescent in situ hybridization (FISH)\r\n* For chronic phase CML patients only:\r\n** Must have failed (no response in 3 months or incomplete response at 6 months) or refused treatment with a tyrosine-kinase inhibitor (TKI)\r\n** Must have failed (defined as incomplete response or relapse) or refused donor lymphocyte infusion (DLI) Pathologically confirmed, relapsed or refractory acute myelogenous leukemia Patients with acute lymphoblastic leukemia (ALL), acute myelogenous leukemia (AML), chronic myelogenous leukemia (CML) with relapsed or refractory disease who are not eligible for stem cell transplantation or other standard therapies Subject has a history of myeloproliferative neoplasm (MPN) including polycythemia vera, myelofibrosis, essential thrombocythemia, or chronic myelogenous leukemia. Current acute or chronic myelogenous leukemia Myeloproliferative disorders to be included:\r\n* Idiopathic myelofibrosis\r\n* Polycythemia vera\r\n* Essential thrombocythemia\r\n* Chronic myelomonocytic leukemia\r\n* Chronic neutrophilic leukemia\r\n* Chronic eosinophilic leukemia\r\n* Philadelphia chromosome-negative chronic myelogenous leukemia (CML)\r\n* Hypereosinophilic syndrome\r\n* Systemic mastocytosis For patients with chronic phase chronic myelogenous leukemia, patient’s disease must have evidence of never responded to or progressed after receiving a tyrosine-kinase inhibitor (e.g. imatinib mesylate) Patients with accelerated phase chronic myelogenous leukemia may have =< 10% blasts in the peripheral smear or bone marrow at study entry Lymphoblastic crisis of chronic myelogenous leukemia (CML) Chronic Myelogenous Leukemia (CML) All subjects with evidence of CNS leukemia must be treated and be in CNS CR to be eligible for trial. Patients with chronic myelogenous leukemia (CML) in myeloid blasts crisis Patients must have morphologically confirmed newly diagnosed acute myelogenous leukemia (AML) with blood or bone marrow disease; patients with only extramedullary disease in the absence of bone marrow or blood involvement are not eligible; note: this protocol uses World Health Organization (WHO) diagnostic criteria for AML; patients with acute promyelocytic leukemia (APL, French-American-British [FAB], M3) or blastic transformation of chronic myelogenous leukemia (CML) are not eligible; patients with known core binding factor (CBF) or fms-like tyrosine kinase 3 (FLT3) related leukemias are eligible for this study, but should preferentially be placed on National Cancer Institute (NCI)-sponsored protocols specific for these subtypes, if available Acute myelogenous leukemia (AML) in 1st or subsequent remission Chronic myelogenous leukemia (CML) Subjects with any of the following will NOT be eligible for study:\r\n* Bone marrow involvement\r\n* Active myelogenous leukemia, or history of myelogenous leukemia\r\n* Pregnancy Be diagnosed with chronic phase chronic myelogenous leukemia (CML) Re-induction of acute myelogenous or lymphocytic leukemia after primary relapse Chronic Myelogenous leukemia Chronic myelogenous leukemia (CML)