If you are found to be eligible to take part in this study, you will take dasatinib by mouth twice a day. If you have mastocytosis, you will take dasatinib by mouth once a day. A treatment cycle will be defined as 4 weeks (28 days) + 7 days. You will be instructed to take dasatinib in the morning (between about 6:00 a.m.-10:00 a.m.) and in the evening (between about 6:00 p.m.-10:00 p.m.).