Is it possible to build an Android conformant calendar app which stores its data as shareable file?

Or is there already one? I don't know Androids calendar infrastructure so maybe my question sounds a bit fuzzy. I dislike (non self hosted) cloud services but I like the ability to share my calendar among devices (and even people). Since I'm not alone I wonder whether someone already built a calendar app which stores it's data (encrypted) in a way which can be shared via Syncthing, Sparkleshare, Dropbox, ... This app would have to 'monitor' changes on this file in order to update itself, notify the user about changes and not overwrite changes 'from outside'. So my question is actually two questions: is (are) there such apps already (and how are they called, so I can search myself) or is this possible in the first place (or why not?).