To repeat what the excellent Jeremy Clarkson said not so long ago (
few hours ago as I type, in fact) in Top Gear, in a bend rear wheel drive card tend to over-steer and front wheel drive tend to under-steer.
To complete what he said it must be added that at the limits of the envelope, the two kind of cars must be treated differently.
And must be treated differently, in kind, even when loaded differently, but I'm not going there or I'll be writing War and Peace II - the Return of the Cossack, here.
Usually though, when a front wheel drive starts over-steering, like I seem to understand you're wondering, slamming the the throttle close and applying opposite lock only is quite the mistake, because the resistance of the engine braking (
which normally is quite useful) will worsen the over-steer no matter how much opposite lock you apply.
I've driven both kind of cars up to the jagged edges of their envelopes and USUALLY when dealing with over-steering front wheel drives (
thing that happens mostly because of contaminated tarmac) you should CUT power to the front wheels with the clutch, leaving them to freely spin, and GENTLY apply a degree of opposite lock to recover.
Applying a bit of power instead CAN be as much as useful, but you
MUST be able to gauge HOW MUCH POWER to apply, or you will end up only exacerbating the problem and losing control.
This, in fact, poses the problem that if you have an automatic, how you recover is up to the behavior of the gear system. If its clutch releases totally at your cutting the power, you can use the same technique listed above, and if it doesn't (
because its advanced system wants to apply engine braking to aid pedal braking, like it is usually done in a manual gear car)... you SHOULD apply a little bit of power, as you hypothesized. The right amount. Which, of course, changes from car to car, from tires to tires, from gear system to gear system, from situation to situation. Just be ready to learn while spinning... which, done in a secure environment, can be quite fun.
Generally speaking, that is.
PS
Never dealt with four wheel drives. Here in south Italy they're the cars of the bombasts, and I'm quite proud not to be one of them.
There is no such a thing as overkill. Only unworthy targets.