Minkey:
This is a silly question. How does the buddy system work when there are three divers? Who's the odd diver? Who watches who? Do you have a designated leader and the other two follow? Do you do a buddy check as if you were toasting champagne to everyone (i.e. each buddy checks the other two)? Or do you grab a single diver who happens to be around?
My buddies and I often dive as three-person teams. There is no odd diver ... well, we're all kind've odd, but as far as the dive team goes we're all pretty equal. We decide in advance who is going to lead. The leader dives in the middle, with a dive partner on either side. We space ourselves about 4-6 feet apart ... a little closer if vis is terrible. Basically, you want to make sure that you can all keep track of each other.
We do that with our lights. Shine your light in front of you where both of your dive buddies can see it ... if they can see your light beam, they don't have to keep looking around for you. If we want our buddies' attention, we use our lights to signal. Light signals are similar to hand signals, except you can "project" them so they're easier to detect.
We do buddy checks as a team ... and that includes doing "bubble checks" on each other by laying back while one of your buddies looks at your first stage, valve, and hoses to make sure you're not leaking. One buddy per bubble check is sufficient, as long as everybody gets checked.
For the most part, with a little practice, 3-person buddy teams are easy ... and as Northeastwrecks pointed out, you have just that much additional safety factor in terms of redundancy and the extra pair of eyes looking out for each other.
... Bob (Grateful Diver)