Another mode I've grown to love from another racing game is 'Cat and Mouse.' It takes the 'Team Pushing' up a few notches.
Each team has a slow car called a 'mouse.' The rest of the team have much faster 'cat' cars. Teams compete to get their mouse across the finish line first. Cats can attack an opposing mouse, defend their mouse, or even push/draft their mouse for a helpful speed increase. A mouse must drive as fast as they can, but also guard against attacking cats.
Because the event is still a race(for the two mice), car choice and track familiarity are important. Because of the combative nature of the game, car choice could become even more critical, along with driver skill. The team aspect also makes for interesting gameplay, as a team of great drivers can still lose due to poor communication/teamwork.
Normally, I've seen this game played with two teams of four. With GT5's capacity for double the players, either more teams or bigger teams could be used to really make this game interesting.