When petitioning for schools to go along with my re-enlistment packet, is there something specific that needs go with it?

You can request classes in conjunction with reenlistment if it is your first reenlistment. Other than that, you can only do that if it is in conjunction with an MOS change. Why not just go to your NCO Support Channel and just ask for whatever class you're looking for. What are you trying to get?

Both of these guys are correct. Your NCO Support Channel should be your first and only option. It would be helpful to know that UMODP (Unit Movement Officer) training and TCAIMS training will nearly always be at least helpful, if not essential. However, every unit is different, at BN and BDE level or even higher there may be individual classes or requirements based upon your mission. Your schools NCO and also possibly your Company Training NCO should be trained in identifying those additional requirements.