I REALLY like the idea of multiple "actions" per turn, especially keyed off of the actions of fellow pcs.
I'd support a mechanic that forces players to pay attention when the other players are taking their turns, ideally by "paying them" with their own chances to do cool things keyed off of others.
I like some of the ways that 4e has done this, and dislike others...I don't think the economy of "turn taking" was the reasoning behind it, though I'd like it to be. The other thing I'd hope for in future development is that the actions really make sense and flow from one another. E.G. Fighter uses pushback, flanking rogue gets an attack of opportunity. NOT Paladin hits a guy, someone else in the party suddenly heals for a hard-to-describe reason.
But, really, there are some indie games out there that do an excellent job of concurrent or triggered turns so that we don't have the paradigm that has been present in most editions...that of "I take my turn, then wait around for quite a while while we go around the circle of initiatives and then I FINALLY get to act again."
Give players an incentive (that of doing cool stuff) to pay attention, and to have fun on not just their own turn, but on others as well. 4e probably has done this the best of the editions so far, but needs some refinement, along with a clear goal of what this rule is there to accomplish.