Copy and paste
I think my use case is maybe a little different, but would be great to solve this problem.
I have a made a big image with lots of tiles. I use this file for drawing concepts for an enemy or a sprite etc. I iterate a lot, making copies of tiles, then changing different things to see what works.
Problem is that once I have come up with a good character, I can see no way of creating a new document and copying one of the tiles to it to start working on the different poses/animations etc.