What you would have to do is make a single document store with multiple views. and it's the views that differ for different people.
Just design a tagging system for the documents and views to compensate, and use a single document store.
In SharePoint you can create views in multiple ways for a list or a library. The document store web part is no exception.
Add a Managed Metadata column to the document store, then add a filter to the view dependent on this column. Your event receiver would then automatically tag the document depending on the location of the web part you are using to view the document store.
Using this method once setup, you can have any number of document stores with a single bucket, and you can control if it is possible to view other virtual document stores with this tag filtering.
This is the SharePoint way, one location for files and one place to collaborate.