Of screens and computers

This post is something of a wish / to do list really.

I already use a couple of screens when I’m working but really would like to have a couple more.

The trouble is I don’t really want one poor struggling PC providing the grunt for all the screens.

Actually I would prefer at least a couple of independent machines running the screens, so I can happily shut one machine down without having to rebuild the entire desktop at start up.
However I’d also like to be able to drag and drop documents between all the screens. Can it be done? I think it might be possible but don’t yet know how.