From my fairly considerable commuting experience I have had:
Slick up mtb, was nice a cheap but heavy ended up spending a bit more than it was worth to get something out of it. Enjoyed it when I got there though.
Fixed wheel, a revolution, again cheap nil maintenance and had the different factor, did become boring after a few years though. All very well saying its great training but not every bleeding time.
Road bike, was quick and light and great for extra post work miles, not really too much wrong with it apart from limiting itself to roads.
CX bike, is current flavour of the month, the more I live with it the better it gets, allowing me to do one of the most important things and thats go different routes. Covers 95% of the terrain in my area.
Anyway I was thinking about it recently and decided that there is no real best bike, I'm going to do up the fixed wheel and fit mudgaurds to an old road bike. The variety keeps the commute interesting as well as the flexibilty. So to surmise you need not one more bike but a few
Knowing what you have you won't regret getting a CX bike and choose one as a tool rather than a desirable object.