My own game, The Sunken Stones, just hit its two year anniversary, and we've been running concurrent groups for about half that time. We implemented it about one year ago, making the second group, and it has worked out well.
There's a catch in this one, though: The players remain the same. Five players, two PCs each. We switch between the parties every other 'chapter', and though they certainly do and can interact together, they are generally so far apart in the game world that overlap has rarely occurred. However, just recently, two PCs from group two just broke off from their party and stumbled upon the original group, so we'll see how that plays out.
There's a catch in this one, though: The players remain the same. Five players, two PCs each. We switch between the parties every other 'chapter', and though they certainly do and can interact together, they are generally so far apart in the game world that overlap has rarely occurred. However, just recently, two PCs from group two just broke off from their party and stumbled upon the original group, so we'll see how that plays out.