What else is in the zip binder? Is it just papers, or does she have a pencil pouch, spiral notebooks, calculator etc in there? If she has other things, taking them out will help reduce the bulk now, but you may be facing the same dilemma in a few months.
If it's already full of just papers, and she's not allowed to remove any, and she has to have "mega binder", then I would ask the teacher(s) for a recommendation. The office stores have 5" binders, but they start at $24,and it has been my experience that no matter the price you pay for a binder, it is the rare binder that actually holds up to daily use, being lugged in a backpack, shoved in a desk/locker and generally knocked about - and the bigger ones perform worse than the smaller ones!