Dasatinib, Temsirolimus, and Cyclophosphamide in Treating Patients With Advanced, Recurrent, or Refractory Solid Tumors

Inclusion Criteria: * Patients must be \>/= 12 months and \< 21 years of age at the time of study enrollment. * Patients must have had a previous histological verification of a solid tumor at the original diagnosis and/or recurrence including brain tumors; for patients with brain stem gliomas and optic pathway tumors, the requirement for histological evaluation may be waived; the patient's disease must be considered refractory to conventional/standard therapy, or a disease for which no conventional therapy exists and is progressive * The patient must have a stable clinical (neurologic in case of brain tumors) exam and be on a stable dose of steroids for at least 1 week prior to study entry; the patient should have a measurable and/or evaluable disease; measurable disease which is defined as the presence of at least one lesion that can be accurately measured in two dimensions (each measures at least 10 mm) or evaluable disease which is defined as at least one lesion that can be accurately measured in at least one dimension (measure at least 10 mm) * Karnofsky performance status \>= 50 for patients \>= 16 years of age and a Lansky performance status \>= 50 for patients aged \< 16 years * Life expectancy: must be \>= 12 weeks * Chemotherapy: * Must not have received myelosuppressive chemotherapy within 3 weeks of the study entry (6 weeks if prior nitrosourea); prior treatment with either dasatinib or temsirolimus but not both is allowed; at least 3 weeks must have elapsed from the last dose * Biologic therapy (anti-neoplastic) * Must not have received oral tyrosine kinase inhibitors (other than dasatinib) or other similar agents within 3 weeks of the study entry and all toxicities must have resolved to \< grade 2 prior to enrollment * Must not have received bevacizumab or other monoclonal antibody therapy within 4 weeks of study the entry * Radiotherapy (XRT): at least 4 weeks for focal XRT or 8 weeks for craniospinal XRT must have elapsed prior to study entry * Stem cell transplant (SCT): at least 8 weeks following autologous SCT and 12 weeks for allogeneic SCT * Surgery: at least 2 weeks following surgery including brain and spine provided post-operative magnetic resonance imaging (MRI) shows no active bleeding * Concomitant medications: the following drugs need to be stopped at the time of beginning therapy: patient cannot be on liver enzyme inducing anticonvulsants; patients must not have received growth factors to support the number or function of white cells or platelets within the past 7 days and pegfilgrastim within the past 14 days; patients must not be receiving any anti-thrombotic or anti-platelet agents; patient cannot be on drugs that cause significant prolonged QT (category I drug) * Absolute neutrophil count (ANC) greater than or equal to 1000/mm\^3 * Platelets greater than or equal to 75,000/mm\^3 (transfusion independent; no transfusion for \>= 7 days prior to study enrollment) * Hemoglobin greater than 8.0 g/dL (transfusion independent; no transfusion for \>= 7 days prior to study enrollment) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 x upper limit of normal for age (ULN) * Bilirubin =\< 1.5 x ULN * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \> 70 ml/min/1.73 m\^2 OR serum creatinine based on age/gender as follows: * Age 1 to \< 2 years, 0.6 mg/dL (male) and 0.6 mg/dL (female) * Age \> 2 and \< 6 years, 0.8 mg/dL(male) and 0.8 mg/dL (female) * Age \> 6 and \< 10 years, 1.0 mg/dL (male) and 1.0 mg/dL (female) * Age \> 10 and \< 13 years, 1.2 mg/dL (male) and 1.2 mg/dL (female) * Age \> 13 and \< 16 years, 1.5 mg/dL (male) and 1.4 mg/dL (female) * Age \> 16 years, 1.7 mg/dL (male) and 1.4 mg/dL (female) * All post-menarchal females must have a negative serum beta-human chorionic gonadotropin (beta HCG); sexually active patients of childbearing potential must agree to use an effective method of contraception during the study and for at least 6 months after * Adequate pulmonary function as defined as: no evidence of dyspnea at rest, no exercise intolerance, and a pulse oximetry \> 94% if there is clinical indication for determination * Adequate cardiac function defined as: normal 12 lead electrocardiogram (EKG) with corrected QT interval (QTc) \< 450 msec, and either shortening fraction of \>= 28% by echocardiogram and qualitatively normal left ventricular function, or ejection fraction of \>= 55% by echocardiogram * Patients with seizure disorder may be enrolled if on non-enzyme inducing anticonvulsants and well controlled * Serum cholesterol and serum triglyceride levels must be \< grade 2 * A written informed consent MUST be obtained from the patients and/or their parents/legal guardians prior to enrollment indicating their awareness of investigational nature of this study Exclusion Criteria: * Patients with evidence of recent intratumoral hemorrhage (within 3 months of study enrollment), gastrointestinal bleeding, history of coronary artery disease or on anticoagulation therapy * Pregnant or breast-feeding women will not be entered on this study * Uncontrolled current illness including, but not limited to, uncontrolled infection, need for hemodialysis, need for ventilatory support, psychiatric illness/social situations that would limit compliance with study requirements * History of hypersensitivity to any component of the formulation * Patients with known human immunodeficiency virus (HIV) are ineligible for this study * Patients must not have received prior therapy with dasatinib and temsirolimus for any indication * Patients with clinically significant cardiovascular disease: history of ischemic or hemorrhagic stroke within past 6 months; uncontrolled hypertension, on at least 2 repeated determinations on separate days within past 3 months; myocardial infarction or unstable angina within past 6 months; New York Heart Association grade III or greater congestive heart failure, serious cardiac arrhythmia requiring medication, unstable angina pectoris within past 6 months; clinically significant peripheral vascular disease within past 6 months; pulmonary embolism, deep vein thrombosis (DVT), or other thromboembolic event within past 6 months; diagnosed congenital long QT syndrome; any history of clinically significant ventricular arrhythmias (such as ventricular tachycardia, ventricular fibrillation, or torsades de pointes); prolonged QTc interval on pre-entry electrocardiogram (\> 450 msec); subjects with hypokalemia or hypomagnesemia if it cannot be corrected prior to dasatinib administration * Anticonvulsants: patients on enzyme inducing anticonvulsants (EIAED) will be excluded; if patients were previously on EIAEDs that have been discontinued, patients must have been off EIAEDs for \>= 2 weeks prior to initiation of dasatinib * Anticoagulants/anti-platelets: patients on therapeutic (treatment) dose of anticoagulants (e.g. warfarin, low molecular-weight heparin) are not eligible; patients are not allowed to take aspirin, clopidogrel, ticlopidine, Aggrenox; patients on prophylactic anticoagulation may be enrolled and treated on study as long as their platelet count is monitored closely and maintained at \> 75,000 while they are receiving dasatinib * Inducers and Inhibitors of cytochrome P450 family 3, subfamily A, polypeptide 4 (CYP3A4): patients required to be on any CYP3A4/5 inhibitors or inducers will be excluded (with the exception of dexamethasone, but all efforts should be made to reduce the dose of dexamethasone); patients must discontinue drug at least 7 days prior to starting dasatinib * Angiotensin-converting enzyme (ACE) inhibitors: patients who are currently receiving ACE inhibitors are not eligible * Anti-graft-versus-host disease (GVHD) or agents to prevent organ rejection post-transplant: patients who are receiving cyclosporine, tacrolimus or other agents to prevent either graft-versus-host disease post bone marrow transplant or organ rejection post-transplant are not eligible for this trial * Category I drugs that are generally accepted to have a risk of causing torsades de pointes including: (patients must discontinue drug at least 7 days prior to starting dasatinib) * Quinidine, procainamide, disopyramide * Amiodarone, sotalol, ibutilide, dofetilide * Chlorpromazine, haloperidol, mesoridazine, thioridazine, pimozide * Cisapride, bepridil, droperidol, arsenic, chloroquine, domperidone, halofantrine, levomethadyl, sparfloxacin, lidoflazine * Other drugs permitted but use with caution include; drugs are not recommended but can be used with caution * Antacids: use of H2 blockers and proton pump inhibitors is not recommended; patients who require antacids should use short acting, locally active agents (e.g., Maalox, Mylanta etc.); however, these agents should not be taken within either 2 hours before or 2 hours after the dasatinib dose * Drugs prolong QT interval; erythromycin, clarithromycin, pentamidine, ondansetron, granisetron, and methadone