Does Anyone know!?!

Ok, so we just picked up a new to us Grand Cherokee, and I found one little problem. I hope some of you can help me out! It has the Quadratrac 4.0L and is a 2001.
When you completely push the accelerator all the way to the floor when taking off, all is good. Until you reach the top of the power band and rev it out, but it will not shift to second. It just bounces back and forth on the rev limiter and still wont shift. It is in Drive and not first.
Any ideas what that could be?
I know that on my XJ I can change the shift points, can I change that as well on the Grand? Can anyone please help me, as I want my girlfriend to be as safe as possible!
Thanks all!!

make sure the tranny has enough fluid in it, when i broke a tranny cooler line mine wouldnt shift out of first, not enough pressure i guess i dunno. at least its somewhere to start. dont keep bouncing it off the rev limiter you're going to ruin the crank or the cam.

i believe the fluid should be good ...
maybe the TPS is acting up?? It only does it in first gear when punched! Can I adjust it?

that's the 42re tranny, they're kind of known for that sort of behaviour. usually it comes down to either the pressure sensor transducer, or the transmission governer solenoid, or both. if it were me, i'd change them both. they're in/on the valve body, not too bad to get to really.