Webstrates are web substrates, a practical realization of shareable dynamic media under which distributability, shareability, and malleability are fundamental software principles. Webstrates blur the distinction between application and document in a way that enables users to share, repurpose, and refit software across a variety of domains, but its reliance on a central server constrains its use; it is at odds with personal and collective control of data; and limits applications to the web. We extend the fundamental principles to include interoperability and sovereignty over data and propose MyWebstrates, an implementation of Webstrates on top of a new, lower-level substrate for synchronization built around local-first software principles. MyWebstrates registers itself in the user’s browser and function as a piece of local software that can selectively synchronise data over sync servers or peer-to-peer connections. We show how MyWebstrates extends Webstrates to enable offline collaborative use, interoperate between Webstrates on non-web technologies such as Unity, and maintain personal and collective sovereignty over data. We demonstrate how this enables new types of applications of Webstrates and discuss limitations of this approach and new challenges that it reveals.