Remember in "Terminator 2: Judgement day", where T1000 chases T101 & John Connor in a storm drain with a huge unstoppable truck and both of them are on motorcycles?
This game should have a mode just like that!
A huge unstoppable truck just rams all cars behind you, leaving a path on both sides (in case you crash) where you need to overtake it and rejoin the actual race. It could also be in a storm-drain-type level, but it works with a rock-wall and cliff too, I suppose.
Combine that with wacky traffic rules or burned car wrecks blocking your way and you have some real '90s movie action right there! All it's missing is a punch-line every time you defeat another driver...
Granted, it would be more about precision driving than actual bike-to-bike combat, but man! - it'd be hilarious!