I haven't find anything like that. In RBR you are always alone on the track, so I think it is imposible, but a superpecial stages are avaliable, but always alone.
There is the RBRNet mod that allows you to race online against others where the other people show up as ghost cars. This does not allow you to use the RSRBR2010 stuff tho, only vanilla RBR.
Nothing like Rallycross in Dirt2, which is exactly what you describe.
Unfortunately RBR only allows one driver at a time. There are a few Super Special Stages where you cross over the track like in the X games, etc, but Jakub is right, you are still alone on the stage.