Can the number of staves per system be varied during a composition?
I think you're asking of you can have a page that has an extra staff added to the score for only part of the piece. For instance, a piano and voice tune might have just two staffs until the voice starts, then it has three.
Unfortunately, no.
A part work-around might be to divide your piece by page, working from the front. You'd need to save each section into a different file, where you can choose which staves to print. It's messy, tedious, and splits your work. I only use it if I really have to have the look correct, or if I have nasty page turns. Even then, I still keep the original as a complete file.
You might be able to print the individual pages one-at-a-time from the same file, but when you adjust the number of printing staves, the pagination would mess up. You'd need to do some serious set-visibility Never, or inserting extra space to make it work.