Inclusion Criteria:

- Histologically confirmed diagnosis of 1 of the following:

- Malignant extracranial solid tumor

- Recurrent or refractory disease

- Known bone marrow metastases* allowed

- Imatinib mesylate-resistant Philadelphia chromosome-positive (Ph+) acute
lymphoblastic leukemia (ALL), defined as M3 bone marrow in a patient who
previously received imatinib mesylate-containing treatment regimen

- Imatinib mesylate-resistant Ph+ chronic myelogenous leukemia (CML), as defined
by any of the following:

- Increasing WBC or platelet count while on imatinib mesylate therapy

- Lack of any cytogenetic response after an adequate duration of imatinib
mesylate therapy, as defined by 1 of the following:

- Failed to achieve a complete hematologic response after completion of
3 months of imatinib mesylate treatment

- Failed to achieve a partial or complete cytogenetic response (i.e., ≤
35% Ph+ cells) after 6 months of imatinib mesylate treatment

- Appearance of accelerated or blastic feature while on imatinib mesylate
therapy

- Reappearance of Ph+ clones after an initial complete cytogenetic response
to imatinib mesylate

- More than 30% increase in Ph+ cells in peripheral blood or bone marrow
cytogenetics while on imatinib mesylate therapy

- Imatinib mesylate intolerance, as defined by development of adverse effects
requiring discontinuation of imatinib mesylate therapy

- Measurable disease (for patients with CML or ALL)

- Determined by hematologic, cytogenetic, and molecular studies for CML

- Determined by bone marrow blast percentage for ALL

- Measurable or evaluable disease (for patients with solid tumors)

- No known curative therapy or survival-prolonging therapy with an acceptable quality
of life

- No CNS solid tumors

- CNS-positive leukemia allowed

- Karnofsky performance status (PS) ≥ 50% (for patients > 10 years of age)

- Lansky PS ≥ 50% (for patients ≤ 10 years of age)

- No evidence of graft-vs-host disease

- Solid tumors:

- Absolute neutrophil count ≥ 1,000/mm^3 (750/mm^3 if bone marrow infiltration)

- Platelet count ≥ 100,000/mm^3 (transfusion independent) (50,000/mm^3 if bone
marrow infiltration)

- Hemoglobin ≥ 8.0 g/dL (red blood cell [RBC] transfusions allowed)

- ALL/CML:

- Platelet count ≥ 20,000/mm^3 (platelet transfusions allowed)

- Hemoglobin ≥ 8.0 g/dL (RBC transfusions allowed)

- Creatinine clearance or radioisotope glomerular filtration rate ≥ 70 mL/min OR
creatinine based on age, as follows:

- No greater than 0.6 mg/dL (1-23 months of age)

- No greater than 0.8 mg/dL (2- 5 years of age)

- No greater than 1.0 mg/dL (6-9 years of age)

- No greater than 1.2 mg/dL (10-12 years of age)

- No greater than 1.4 mg/dL (13 years of age and over [female])

- No greater than 1.5 mg/dL (13-15 years of age [male])

- No greater than 1.7 mg/dL (16 years of age and over [male])

- Bilirubin ≤ 1.5 times upper limit of normal (ULN)

- ALT ≤ 110 U/L

- Albumin ≥ 2 g/dL

- Normal 12-lead EKG with corrected QTc < 450 msec AND meets 1 of the following
criteria:

- Shortening fraction normal

- Ejection fraction normal

- No evidence of dyspnea at rest

- No exercise intolerance

- Pulse oximetry > 94% if there is a clinical indication for determination

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception

- No uncontrolled infection

- No swallowing dysfunction that would prevent taking an oral or liquid medication

- See Disease Characteristics

- Recovered from prior chemotherapy, immunotherapy, or radiotherapy

- No myelosuppressive chemotherapy within the past 3 weeks (6 weeks for nitrosoureas)

- At least 7 days since prior growth factors

- At least 14 days since prior pegfilgrastim

- At least 7 days since prior biologic agents

- At least 2 weeks since prior local small-port palliative radiotherapy

- At least 3 months since prior total-body irradiation, craniospinal radiation, or
radiation to ≥ 50% of the pelvis

- At least 6 weeks since other prior substantial bone marrow radiation

- At least 3 months since prior stem cell transplantation

- Hydroxyurea cytoreduction for Ph+ leukemia allowed provided it is discontinued 24
hours before first dose of dasatinib

- Prior intrathecal (IT) therapy allowed (for patients with CNS-positive leukemia)

- Concurrent IT therapy comprising hydrocortisone, cytarabine, methotrexate, or
cytarabine (liposomal) allowed (for patients with CNS-positive leukemia)

- No other concurrent investigational drugs

- No other concurrent anticancer agents, including chemotherapy, radiotherapy,
immunotherapy, or biologic therapy

- No concurrent enzyme-inducing anticonvulsants, including any of the following:

- Phenytoin

- Phenobarbital

- Carbamazepine

- Felbamate

- Primdone

- Oxcarbazepine

- No concurrent antithrombotic or antiplatelet agents, including any of the following:

- Warfarin

- Heparin

- Low-molecular weight heparin

- Aspirin

- Ibuprofen

- Other nonsteroidal anti-inflammatory drugs

- No concurrent CYP3A4 inhibitors, including itraconazole, ketoconazole, and
voriconazole

- No concurrent highly active antiretroviral treatment for HIV-positive patients