As Buddy got bigger, the whole cage (as it was a small hamster cage) became his nest. Draven pulled an old shirt over the whole thing, and put old clothes in it for bedding. We gave him a whole room to himself to run around in. He had already started using our 2 stools as trees, bouncing from one rung to the other, and running in circles around the side of the padded seat. He also would run over every surface of the couch, even upside-down under the cushion. We gave him the stools, but kept the couch for ourselves. I also hung an old blanket up on the wall so that he has something to run up and down, hide behind, and lounge on top of.
We soon found out we had no problem with "toilet training" him, as he choose the farthest corner in the room to pee. So long as you keep corners well papered, it is not a problem. A few times when he was out in the main room, he would turn around and back himself into the corner. That is when one of us would go running over, scoop him up and deposit him in the corner of his room with the paper. I have no idea if this is habit for all squirrels, but we found it very handy. Later I found out that ferrets will do this also. Perhaps some ferret instructions then also can apply to squirrels, but use your head! Toilet training and teaching them not to bite hard seem the most applicable.
Squirrel-proofing the room...