MRs have a tendancy to produce snap oversteer.
Meaning when you correct one oversteer, if you over correct, you'll end up "snapping" into an oversteer on the opposite (or reflected, actually) angle.
This is actually a really nice way to do multiple drifting.
If you've ever read Initial D, the way tak does doubles is by using snap oversteer.
Professional drifters (Like in Formula D) also use this alot.
But it's very hard to control, due to the snapping action.
But anywho, once you replace the suspension your problems should go away. Just make sure to set it up right and tune the setup at an auto-x (or in an empty parking lot =P ).
With a proper suspension setup you should be beating the CRX on the straights and downright rocking it through the corners.
What you should do is practice some drifting, then when you race your buddy again charge hard into a sharp corner and do an outside braking pass (otherwise known as a running drift). Of course, you could probably just skip the theatrics... but you would certainly surprise your friend if oyu pulled it off