I did have played in (and sometimes run) in a shared Thousand Suns game between a few groups. The characters were all 1970's Space Opera characters who did illegal things across the setting. Each group had their own ship and they worked within the same scope of authority and ring of contacts so that the effects of each large movement would be felt among each crew.
I've also done this with FATE in a fantasy setting where all players would switch out and run a session, making sure that everyone only ran one session in a row to ensure that the strings that coiled the world together were cluttered, muddled, and ridiculous. It worked well because no one ever mentioned who was missing or that someone was not present in a previous adventure.
"Wait, Princess Falisia Moonbeam is the vampire Hourglass? Then who controls the globe of tides?"
"The Pirate Lord Granacht of Brunsmark—who is meeting with the Unicorn Varsuvious this very day at the Part-tide Festival in the Vale!"
I find that you want their to be a definite discourse between the groups, but not so much as to force actions.