With three teams the whole concept doesn't work. You need an absolute man advantage to sell the drama with the sway of momentum. Even worse with three teams there will be very little gamesmanship, and the build to a new entrance just won't work. When it's 4 on 3 or 2 on 1 shit is exciting waiting for the odds to stack up. With 2-2-2 the next guy doesn't make too much difference, even the first winning entrant (usually the biggest story element) is basically walking into a tag match.
This isn't complicated, they tried this shit in 98 and with seven Hall of Famers (sorry Lex Luger and Stevie Ray) it was balls.