More of a career mode.
Season on season career advancement, with drivers moving between teams, maybe a driver pool to fill in gaps, and the player getting offers from other teams as well as contract extension offers, first and second drivers who get different access to upgrades perhaps (think Mark Webber), so you could be offered a first driver role at Williams or a second driver at Red Bull after the same experience.
Also, more retirements. Pushing too hard increases engine or gear box burn out for example, leading to failure or the need to change parts (and incur grid penalties). Perhaps a reliability upgrade. Random crashes. Changing yellow flag to safety car too!
Thanks Jack - some really good stuff there.