Patients with malignant pleural effusions that do not resolve after first-line systemic therapy. Patients with pleural effusions that have become too small for thoracentesis at the time of registration would be permitted on study, indicating a significant response to first-line systemic therapy. Exudative, bloody, or cytological proven malignant effusions Uncontrolled symptomatic ascites or pleural effusions within months. Patients with significant visceral fluid collections including ascites, pericardial effusions, pleural effusions or others may experience delayed clearance of methotrexate and inability tolerate the proposed study treatment; while these are not absolute exclusions the Study Chair or co-Chairs should be contacted to discuss possible enrollment; patients with significant ascites defined as European Association for the Study of the Liver >= grade , or with asymptomatic pleural effusions with an estimated size > mL, or with symptomatic pleural effusion of any size will be excluded Patients with clinically significant ascites or pleural effusions. Greater than minimal, exudative, or cytologically positive pleural effusions Chylous effusions associated with malignant disease Patients with advanced/metastatic disease who have symptomatic visceral spread, and who have life threatening complications needing immediate therapy, such as massive uncontrolled effusions [pleural, pericardial, peritoneal], pulmonary lymphangitis, and over % liver replacement with tumor. The presence of lung, liver, or known brain metastases, malignant pleural effusions, or malignant ascites Patients with documented significant pleural or pericardial effusions unless they are thought to be secondary to their leukemia. Symptomatic pleural effusions or ascites (requiring constant or intermittent drainage) Clinically significant and/or rapidly accumulating ascites, pericardial and/or pleural effusions; mild ascites that does not preclude safe tumor biopsy as protocol specified is allowed at the discretion of the treating physician Pleural effusions or ascites. Patients with documented significant pleural or pericardial effusions unless they are thought to be secondary to their leukemia. High volume peritoneal or pleural effusions requiring a tap more frequently than every days; moderate to severe ascites Any clinical or radiological ascites or pleural effusions Patients with large and recurrent pleural or peritoneal effusions requiring frequent drainage (e.g. weekly) Subjects with malignant pleural effusions and malignant ascites Patients with clinically significant pleural or pericardial effusions Patients with documented significant pleural or pericardial effusions unless they are thought to be secondary to their leukemia Presence of pleural effusions > mm as measured by treating physician using standard radiologic measuring tools Recent history (within months) of uncontrolled symptomatic ascites or pleural effusions. Pleural effusions that are minimal (i.e. not visible on chest x-ray) that are too small to safely tap are eligible Patients with symptomatic effusions (pleural, pericardial, or peritoneal) and/or those who have required a procedure for symptomatic effusions within weeks of start of dasatinib are ineligible The presence of liver, or known brain metastases, malignant pleural effusions, or malignant ascites Symptomatic ascites or pleural effusions Exudative, bloody, or cytologically malignant effusions If pleural fluid is visible on CT scan thoracentesis to exclude malignancy should be obtained. Patients with effusions that are too small to tap are eligible. Greater than minimal, exudative, or cytologically positive pleural effusions History of ascites or pleural effusions, unless successfully treated. Symptomatic effusions due to pleural, pericardial, or peritoneal metastasis of epithelial ovarian cancer Patients with known moderate/severe pleural effusions that are unrelated to malignancy or established diagnosis of pulmonary arterial hypertension The presence of known brain metastases, malignant pleural effusions, or malignant ascites; brain MRI is required at screening only if clinically indicated Patients with clinically significant pleural or pericardial effusions Patients with symptomatic effusions on account of pleural, pericardial or peritoneal metastases of melanoma Known presence of central nervous system metastases, pleural effusions or ascites Patients with a history of malignant pleural effusions are not eligible; pleural effusions considered by the investigator too small for a diagnostic thoracentesis are permissible Patients with documented significant pleural or pericardial effusions unless they are thought to be secondary to their leukemia Exudative, bloody, or cytologically malignant effusions Patients with malignant pleural effusions or significant pericardial effusions Patients with symptomatic effusions on account of pleural, pericardial or peritoneal metastases of melanoma Ascites, pleural effusions, or osteoblastic bone metastases as the only site of disease. Presence of large accumulation of ascites or pleural effusions, which would be a contraindication to the administration of methotrexate for GVHD prophylaxis Recent history (within months) of uncontrolled symptomatic ascites or pleural effusions. All patients whom do not have malignant pleural effusions Subject has bilateral pleural effusions, with both being at least moderate in size (greater than one-third of the hemithorax on CXR). Chylous effusions associated with malignant disease Epithelial ovarian cancer outside of the peritoneal cavity, with the exception of pleural effusions Body cavity effusions not caused by primary effusion lymphoma nor chylous effusions directly related to lymphatic infiltration by KS