When the iTunes Store music was DRM'ed, this was a problem. But these days, your problem boils down to sharing the raw files for the music, and adding the directory containing those files to iTunes. Probably you're interested in the functionality of iTunes so that it can automatically "discover" music that has been added to a directory. I think that exists, but I haven't used it do far, so I don't know the details.
If some of your music is older and has access restrictions on it, then you have a bigger issue to work around. You can try to remove the protection. But otherwise, I don't a way to share protected music files and sync them together.