Yes, but it all has to happen in the same phase. If somebody with a Reflexes of D10 splits his attacks, whereas he can normally move 20 feet per phase, I might rule that each split divides that movement further. Splitting dice for two attacks might reduce that movement in the phase to 10 feet, and three down to six feet or so.
Do you really keep track of movement in individual phases? That seems waaay too complicated to me (but what do I know?--I haven't played it!).
How about saying that a split attack (and an extra attack if possible) can only be done when no other actions (including movement) are performed in a round?
Do I? Nah, I don't track movement like that, at least not all of the time. If I stated to a player that an enemey was far away, and he asks, "how many feet?", then I'll keep track of that guy until it doesn't matter anymore. So, every now and then movement per phase will come into play, but only when I'm trying to be fair about who gets to attack first. If I got more specific than that, I'd have to use a battle mat, and I'd rather just sketch the battle field out on a dry erase board if absolutely needed.