How much horsepower can a stock 700r4 handle? I am probably only making around 300hp to the wheels so I dont think I have anything to worry about.

mine took 288rhp no problem

but like anything else if you don't want it to break then build a stronger tranny

Stock won't go over 400 hp. However, it would be smart not to try to push it. Get it rebuilt to handle the driving you are doing. You need a corvette servo, and stronger clutches, at the minimum.