I am also struggling to understand this.

1. You can use the "Imposition" Casus Belli as long as you don't claim EVERY inhabited system in the target empire. So you claim all but one near-useless backwater world. In this case you'll get to keep what you claim and the target rump state ends up subjugated. The downside here is the limit on divided loyalties with too many subjects; it's better to have 3-5 large subject states instead of a dozen single-system ones IMO (in addition to Chommel and Tapani Sectors, I like to rapidly subjugate Corellia and Eriadu).

2. Become the Crisis. I'm still not sure if this allows you to attack members of the "Galactic Imperium", because I have my hands full fighting off all the empires that joined the Rebellion. The good news is that you don't even need claims, the systems just change hands as soon as you invade all the planets.

Note: neither of these is a perfect solution. For example, in my current game a Jedi Master appeared on Rendili. At first I kept sending Darth Vader to kill/capture them but Darth Vader died every time no matter how much I save-scummed, so I said "screw it I'll just ignore this one Jedi Master..." Well she ends up leading an insurrection on Rendili and I lost the entire system (very early in the game mind you), **and could not invade it because it was a single-system empire so the Imposition Casus Belli can't be used**. Then they joined the Galactic Imperium so I can't use any of the Senate mechanics to launch a crusade against them either.