pretty sure the answer is "as many as we can figure out how to get the mass for".
absent dismantling the gas giants themselves, you're not going to do anything very interesting do the dynamics of the solar system, regardless of what you take apart, or how you reconstitute it.
and the man-made structures can include mechanisms for closed-loop control of their position. which they'd need anyways, as they'd accumulate positional error from vehicles coming and going.