The first part of the study will involve finding the highest dose of dasatinib that can be given with osimertinib without causing severe side effects, finding out the side effects seen by giving dasatinib at different dose levels with osimertinib, and measuring the levels of dasatinib and osimertinib in blood at different dose levels. The second part will determine the effects of the combination of dasatinib and osimertinib and determine if the amount of Cripto-1 protein in your tumor or blood makes you more likely to have a good response to the combination of dasatinib and osimertinib.