But to try to get back to the original point, I think that no matter what, the important question is not "how closely can it be staked?" but "how closely can it be built?"
That depends largely on the type of building and how it is constructed. If it is one of those prefabricated metal buildings, then it will probably end up being pretty close to plan. If it's built entirely in-place and has a masonry facade or something like that, then you can get rather significant variations.
Then keep in mind that the same issues apply to the asbuilts of the existing building. Sometimes it is really hard to tell exactly where the building edge or building corner lies. It is often quite easy to fudge 0.1' or more just with that. Add to that the fact that building walls can easily drift 0.2' or more either way along their length, and it becomes quite easy to have significant error in the asbuilt of the existing building.
How tight exactly are you talking? Is it a situation where you have less than one foot of wiggle-room? When placing buildings, we generally try to put them at least 1 foot from setbacks and easements, just to be safe, but that's a pretty generous buffer. I'd still want to leave at least 0.5', again just because the repurcussions are so bad if the building is built wrong. But if you don't even have 0.5', then the most important thing is how it is being constructed, out of what kind of materials, and does it have a facade. And know that you are in dangerous territory.