Potential pitfalls:
The scale of change at one table vastly outpacing or overshadowing another table. Make sure that one table doesn’t get to go after the Galactic Overlord while the other tables are trying to fix the irrigation pump. Keep the challenges and rewards roughly in-scale and don’t be afraid to preclude some options that broadly effect everyone without any advance warning.
I would not allow folks to switch table once the event begins, and especially avoid it while games are underway. Give each table a satisfying arc from start to finish across the multiple games, and if you’re time-jumping make sure there’s some compelling continuity to tie the sessions together.
I’d avoid allowing tables to communicate with each other, or allow it only in an explicitly limited manner that either happens at a proscribed time (a ten-minute epistolary break halfway through, maybe) or comes with an unpredictable time delay (so that tables don’t have to interrupt their narrative to respond).
BEST PRACTICES:
Make sure the GMS have a chat before each session about where they’re going and a quick debrief afterwards. Consider a roaming co-ordinator to move between tables and offer advice and assistance and help with continuity depending on how much you value it.
Consider knocking off 15 minutes early to get everyone together to see who their various table affected the world. This requires real work and discipline, you need GMs willing to cut stuff short to make it happen the right way.
Get as close as you can to requiring anyone who registers to play in all the slots. Continuity of players will really help with creating the sense of an ongoing, connected narrative.
Finally, I would very strongly recommend that you stick to the same system throughout. You’ll get much better pick-up, stronger continuity, and have a far better shot at recruiting GMs who’ll deliver consistently. If you’re deeply immersed in the hobby, it can get easy to forget that asking folks to GM 3 or 4 sessions is a heavy lift, but asking them to know 3 or 4 different systems well enough to do it is approaching unreasonable.
Good luck! These events are trickier than they appear, but when you pull them off, they’re amazing.