Schema mappings come in different flavors: simple correspondences are produced by schema matchers, intensional mappings are used for schema integration. However, the execution of mappings requires a formalization based on the extensional semantics of models. This problem is aggravated if multiple metamodels are involved. In this paper we present extensional mappings, that are based on second order tuple generating dependencies, between models in our Generic Role-based Metamodel GeRoMe. By using a generic metamodel, our mappings support data translation between heterogeneous metamodels. Our mapping representation provides grouping functionalities that allow for complete restructuring of data, which is necessary for handling nested data structures such as XML and object oriented models. Furthermore, we present an algorithm for mapping composition and optimization of the composition result. To verify the genericness, correctness, and composability of our approach we implemented a data tr...