Yup, second TOGA push gives full max rated take off thrust. Do not use if you use a fixed derate setting since it will give max rated thrust and therefore could violate the reduced Vmcg.
Second TOGA push removes a thrust reduction only not a derate i.e. a flex or assumed reduction. If you are on a derate takeoff the second push will only go to that derate max.
I you decide that you need more than the derate you will have to manually apply more. Then as Denti said be cautious of Vmcg.
For our B733 operation CatII = autoland = dual autopilot