Rather than having a truly live debate where a question is asked and the candidates speak one at a time, with each one hearing what the one before said, put each candidate in his own studio (or better yet his own sound-isolated section of the studio -- it would be really cool if all of the candidates could still see and be seen by the same audience but they couldn't see and hear each other). A question is asked, and each candidate gets a short time (say five minutes) to prepare, and then they simultaneously get a set amount of time (say two minutes) to answer. The answers are recorded on video, and then presented to the whole audience in random order. For the TV audience, the preparation time is edited out. Optionally after the initial answers are read, the barriers between the candidates are removed and they get a certain amount of time to actually interact with each other.
The advantages I see of this form are that it removes the pressure on the candidates to come up with an instant answer but on the other hand increases the pressure on them to come up with an intelligent answer because they got a little bit of time to think about it, and that it makes it much harder for the candidates to use their answers to attack each other, because they don't know what order they will be heard in and they risk looking dumb if they attack what they think the other guy will say and he actually says something different -- they're almost forced to speak to the question instead of each other.