Martial Alliances should let you fight fellow Federation Members with a special CB
Military Exercise CB, that requires all participants to be at peace and for them all accept with a vote.
Can't take territory (maybe with a new Federation Law?), planets will automatically surrender, all ships get a large bonus to combat disengagement (not perfect escape, accidents still happen), and the winner gets a bonus during the next Federation Leader Election (or depending on the laws immediately becomes the President). Federation Fleet is exempt (temporarily made into an enclave for the duration of the war?), immediate White Peace via event in case outsiders declare war on the federation.
As the name implies, it's meant to be a "fake" war to get their fleets to earn more experience, with everyone agreeing to certain rules to minimize damage, with the main costs being repair the ships after battles are over. It can eventually become more important as the federation levels up (member nations begin the trust one another), with specific laws changing up the particulars like being able to exchange systems (with a vastly increased score cost.)