I know that the RX-8, RSX, Viper, and Z cannot have the wheels changed, and same with the 6 F1 cars, and I guessed on the Vanquish, because I haven't used that car in a while.
That's what I know.
And, if you use the $1 car codes to buy the cars from the dealer, you can change wheels on the RX-8, RSX, Z, and Viper and maybe Vanquish, so that brings the total to 6, give or take several cars.
You're getting closer! All you need to do is just narrow it down a little bit more and you'll have it. Think. These __ cars will always look EXACTLY the same (without cheats).
Alright, I think I know where you might be going with this....
The Z and Viper concept cannot have wheels changed, and cannot have color changed. So, that's 2 since F1 cars are diff. colors, turing cars are same color, but can have wheels changed.
How could it be a Supra, or a Skyline(Skyline's are rare as hell unless you live in Japan, Supra's are almost as rare as Skylines)? What exactly does, "the fastest version of the car comes only as one color?" Plus, I don't think it's a Supra because on GT3 I've maxed both the Supra, and 3kGT VR-4 out, and the VR-4 has way more hp...
the Mazda 787 or ssomething, the DTM cars (Opel Calibra, Opel Astra, Mercedes DTM car) etc 
