Problem with having a war with syndicate, as I recently discovered, is in warscore. To enforce your demands when expelling syndicate you immediately have -150 warscore modifier: -100 for 'demanding surrender', which is usually counter-balanced by war exhaustion, but then you have additional -50 for 'expel wargoal'. And to get these 50 points you have to both utterly destroy their fleet and occupy most of their territory. And if said syndicate have an ally - you could forget about enforcing your demands. I found it much better to settle on 'status quo', since in this case the syndicate get back 1000 credits for every branch office, but it's not me who pays that. And status quo requires very little warscore.
Another problem with syndicates is not every empire have 'impose ideology' wargoal. So, if you have a neighboring syndicate empire, there are only 2 things you can do to stop these pesky branch offices - wage war with said syndicate every time truce ends and settle with status quo as quick as possible, or wipe out the syndicate completely, take all his possessions for yourself or make a vassal out of them.
And if you can't get to the syndicate 'by foot'.. Well, then you just have to suffer the penalties. It's not that terrible, since in most cases crime could be fixed by having only 1 upgraded police station+crime fight campaign. You loose a building slot and a bit of credits, but if your crime is 0 the branch office would auto-shut down sooner or later. The problem with this is the fact that on a 80-pop planet branch office could generate up to 200 crime if I recall correctly. Which would be barely balanced by upgraded police station+enforcers from the capital building, even with 'crime fight' planetary edict.