can you do a simple pull down stairs from the closet to the attic? That may be the most cost-effective.

"I do have a attic above the closet and started thinking about raising the ceiling. "

The ceiling joists are usually the problem.

If it is conventionally framed you can alter them by doubling and removing sections, if they are trusses you need an engineers stamp for any alterations.

started thinking about raising the ceiling

When I build ten-foot ceilings, I always drop them at least a foot in the closet. It's just too difficult to access the extra height and it looks ridiculous. For nine-foot closets you can put in another shelf that can be useful.