I suggest to add some cars into different points of map, like in singleplayer:
For example on beach near the RCbandits racing tracks. Need to create a menu for chosing between mode (1. with computer, like in singleplayer. 2. with other players)
Suggestiable system for the second mode. In this mode first sits driver and choose the number of laps, the limit of players (from 2 to 5) and waiting for other players will join). Other players have to sit in Top fun car by passenger to be joined to racing. And to start playing they have to accept challenge in menu, which will appear, when he will sit in car. Then first player choose "START RACE" and it begins. The winner get some money award, or may be even bonus for best time.
Something the same you can do with RC hellies (don't remember ).
For example: who first will get bombs to a point (remember mission?), or you can get bombs there for time.