There was a time back when my father was racing in Formula Vee, all you needed to comply with the regulations was the engine and running gear to a certain spec. Bodywork was left up to the owner of the car, and as time went on, and ideas around aerodynamics developed (and pieces needed replacing because oops), each car developed its own distinct look.
What I'm proposing isn't so much a new car, but varying bodywork for a few of the existing cars. Small variations that would still fit within the existing collision boxes and that have no real effect on performance, but would add a nice visual variation to the grid when used in different combinations.
Done subtly, they wouldn't interfere with most existing skins, or add any extra pieces that need accounting for - with the exception of air-foils maybe.
The image attached is from the 2015
NZ Honda cup season - this is a great little entry-level series, with lots of variation in models and years. There's at least one civic from every 3-door model they've produced in that field somewhere...