That's more or less what FogCreek did with Trello and CoPilot. While FogBugz was "good enough" to more or less run on rails, they made other bets to expand or productize some of their internal toolkit. It worked so well that these side-bets eventually got much bigger than FogBugz.
I wish more people tried that, instead of messing with their cash-cows. Yes, sometimes you have to keep up with competition or "innovate" in your own space, but if you got big already, chances are that you've done your best work already - leave it as it is and move on.