For once I think politics could actually learn something from sports:
In nearly every sport, it is fundamentally impossible to play more than two teams against each other in a single game. And even if the rules actually somehow allow for it, doing so complicates the process dramatically, usually causing very few wins to truly feel like wins (a team's loss can be blamed on the other losing teams somehow, for example).
So what do they do? Two teams at a time, with some sort of regular season and/or tournament system to give everyone a fair(ish) chance. No, you might not see every single matchup possible, but each team will have to play a variety of other teams with various strengths and weaknesses. Especially in the regular season (in contrast with tournaments, where a team might get an unlucky matchup the very first round).
Applied to debates? One-on-one debates between candidates, randomly chosen and spaced out over time. (edit: I see Inny Binny already made a similar suggestion as I was typing. Yay for convergent ideas!) Tournament stuff has to be ignored, of course, because that's what actual voting is for. That means more time per candidate without actually increasing the number of debates a candidate has to attend (it's been getting pretty insane this cycle). Perhaps even some of the lesser-known candidates can get into debates without actually stressing the system. (10+ candidates in a single debate is disfunctional; even 8 is bad enough.)
But of course, I'm sure that doesn't fit into the media's agendas sufficiently (as others have already noted), so it's not actually gonna happen. For one, I doubt numerous one-on-one debates are going to draw a large audience, so network/cable TV stations would rather just play their regular shows instead of lots of debates. Secondly, they obvious like to have a large manipulating presence in the election process, and a fair system reduces their ability to manipulate, so I don't expect them to shoot themselves in the foot, as much as I'd love to see it.