In the last years, polystore databases have been proposed to cope with the challenges stemming from increasingly dynamic and heterogeneous workloads. A polystore database provides a logical schema to the application, but materializes data in different data stores, different data models, and different physical schemas. When the access pattern to data changes, the polystore can decide to migrate data from one store to the other or from one data model to another. This necessitates a schema evolution in one or several data stores and the subsequent migration of data. Similarly, when applications change, the global schema might have to be changed as well, with similar consequences on local data stores in terms of schema evolution and data migration. However, the aspect of schema evolution in a polystore database has so far largely been neglected. In this paper, we present the challenges imposed by schema evolution and data migration in Polypheny-DB, a distributed polystore database. With our work-in-progress approach called PolyMigrate, we show how schema evolution and data migration affect the different layers of a distributed polystore and we identify different approaches to effectively and efficiently propagate these changes to the underlying stores.