In motorsport, Rivalry between Teams or drivers is part of the game.
What would you think to introduce a Rivalry option inside our Championships and link it to race objectives based on sponsors ?
Instead of having always the same "finish the race in x position" it could be fun to add some new objectives such as :
"Beat your rival by 2 positions"
"Beat team X with at least 1 driver"
"Win this race 2 sec in front of X"
To be fair, your rival should be next to you in the previous league table to avoid strong team vs weak team.