I have rarely made dives as a team of three, but on occasion, it has come up. For me, it's usually myself and a relatively inexperienced (or at least, seemingly less adept) buddy pair. In that type of situation, I find the "tail-dragger" formation works quite well. I put them with each other and tell them that their primary responsibility is to each other, and that I'll be a "plus one". We cover my light signals and audible signals (basically, if they're not too skilled, at a minimum it comes down to "any of these mean stop and look at me"). Then on the dive, it comes down to making sure they're paying attention to each other (and prompting them if I see they haven't been exchanging pressures or other important info).
If they aren't confident enough to lead the dive, of course, I'll lead the dive and keep vigilant watch over both of them. That should only be a stepping stone to help them become comfortable enough in the water and with their communication that they can work together. Once they're communicating well, we'll dive the tail-dragger formation to let them get used to thinking for themselves.
Obviously, this isn't true team diving. It's basically buddy diving with a more experienced diver watching over the dive, but it can be a useful way of helping the less adept divers build their skills. I've found that it often doesn't take too many dives as as a pair-plus-one before the pair is communicating well enough that the group naturally morphs into a threesome with full communication throughout (instead of a pair-plus-one, with limited communication to the one).
So, basically, you start in tricycle formation, with one "dive leader" and two following divers, with the dive leader doing all the thinking (monitoring separation distances, checking pressures, and so on). Then as the two followers gain skills and confidence, you transition to a tail-dragger formation, with the buddy pair doing the thinking (one may be "in charge" for the dive or at any given point therein) and the "dive monitor" following. And finally you transition to threesome formation, diving and making decisions as a team.