Prepare all the components in advance and assemble and bake tomorrow. If you're breading the eggplant, I would also do that tomorrow, since eggplants hold a lot of water and will probably make the crust soggy overnight. Be sure to give the eggplant plenty of time and salt to sweat out so it doesn't end up spongy.

I think it'll get soggy.

I think what I would do is prepare the eggplant, drain it well, grate the cheeses and prepare the sauce, and refrigerate them separately. Then tomorrow I would bring everything to room temperature, layer the eggplant, sauce and cheeses, and bake it just before serving. Leftover eggplant parmesan is OK as leftovers but it's not as good as fresh-baked (imho).