You can get 12 extra cars by doing the following:

Street Rocket - Beat the Novice Circuit
Taxi Cab - Beat the Amateur Circut.
Pickup - Beat the Professional Circut.
Ambulance - Beat the Legend Circut.
Baja Buggy - Beat the Time Trial for Destruction Junction with Street Rocket.
Rag Top - Beat the Time Trial for Alpine Ridge with Baja Buggy.
Blue Demon - Beat the Time Trial for Seascape Sprint with Ragtop.
Hatchback - Beat the Time Trial for Terminal Impact with Ragtop.
Low Rider - Beat the Time Trial for Metro Challenge with Ragtop.
Woody Wagon - Beat the Time Trial for Bayou Run with Ragtop.
Hot Rod - Beat the Time Trial for Sunset Canyon with Ragtop.
Police Car - Beat the Time Trial for Midnyte Rumble with Hot Rod.