Dasatinib in Treating Young Patients With Recurrent or Refractory Solid Tumors or Philadelphia Chromosome-Positive Acute Lymphoblastic Leukemia or Chronic Myelogenous Leukemia That Did Not Respond to Imatinib Mesylate

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