And if it is possible, how would you configure each daemon - graph location, images location, etc?
Great question! It is possible to start a Docker daemon inside a container. In that container you would be able to start more containers. This way you can run docker daemons with different settings on the same host machine.
Checkout this project: https://github.com/jpetazzo/dind. It provides a Docker image that contains Docker itself, just as you require.