I apologize in advance is this is too basic. I do not want to sound patronizing.
In cars with over 200 or 300 hp all under steer (well, most under steer) comes from acceleration. Weight transfer leaves your front wheels without...well, weight. You have to squeeeeeeeeeeeze the throttle.
Even in a Camaro or a Mustang, when you accelerate you are left almost without traction on frontal wheels. That's the reason why dragsters have those ridiculous thin frontal wheels: you use them very little, the weight is all in the rear.
Larry Dixon, 1969: look, ma! No steering!
You must have felt it when taking a curve to the limit: at the exit, you see the edge coming towards you and you instinctively release the throttle. It's not the speed, is the lack of grip.
That's why I mentioned that some drivers tap the brakes on exit, even when accelerating, to "settle down" or "force down" the front axle a bit to diminish oversteer.
Same goes for braking and over steer: you brake too much, you have no grip on the rear axle. The cause is the transfer of weight. I apologize again if this is too basic:
At most racing schools this is the first lesson.
A way to counteract effectively this tendency is to get a lower car.
Of course, acceleration also causes extra torque, like this, but this is kind of secondary.
Acceleration torque: it helps a bit
The reason why in racing you want lower cars, ballast, pull rod suspensions, smaller drivers and down force is NOT to avoid the car from flopping,
but to brake and accelerate in a better way in a curve.
That's the reason why SUVs suck at safety: they brake poorly. You brake mostly with your front wheels, because the CG is high. The higher the car, the worse it brakes.
Next time you see the skids in an accident, notice that rear wheels do not left marks in the pavement (or they are interrupted, when the car rear axle "jumps" in short jumps when you have old ABSs).
I've never raced a car that suffers of under steer in the entrance of a curve, most cars have more weight in the front. That is, I've never racing a car with a rear engine (perhaps a VW?).
So, if your car suffers from under steer in the entrance, well, it's easy to recover confidence: brake, and you'll get all the over steer you could wish.