The best thing to do is talk to your T about this. I have heard of people who have two Ts - usually one for a special issue. My T wanted me to do this, but I was too afraid. But from what I heard, it can work. Also, the other T (if ethical) will not work with you if you are under the care of another T unless that T has signed off on it.

Bottom line is that you can indeed benifit from having two Ts. But you have to be honest with the one you have and let him help you work into this option.