One of my favorite things about Genesys/SWRPG was how initiative worked. For those unfamiliar, you rolled it much like other games, but rather than "Chewbacca goes first, then Greedo, then his henchman, then Han Solo," you generate slots that anyone on your "team" could use. So, in the example, it would go "Hero, Villain, Villain, Hero," thus allowing Han to Shoot First, and all is right in the Galaxy.
A clever group that paid attention could get quite an interesting dance going, especially if they controlled both the top and bottom of the initiative order. You could also take advantage of effects that last until the end of a particular character's turn. I was a little disappointed that they didn't use this system for L5R.
But would it screw things up too badly if we used it anyway? Yeah it could be "abused." But for the most part I would like to reward tactical thinking. For example, there's an ability that knocks your enemy prone, or deals extra damage if he's already prone (Rushing Avalanche?). Usually, your enemy will use his turn to stand up, so you have to knock him down again. However, if you go after him on Turn 1, and before him on Turn 2, you can make mincemeat out of the guy. Seems alright to me.
I think I would require that everyone act on their rolled slot on the first turn of combat, and obviously this wouldn't work in duels (bit you manipulate Initiative every round anyway). But other than that, nothing game-breaking jumps out at me.