Frankly, stop buying coat hangers.
It serves as an alert that:
a. It's time to clean out and donate.
or
b. We don't need anything new.
or
c. Both!
So pick a number of coat hangers to start.
(Preferably a number that fits comfortably in your closet.)
Then stick with it.
Don't buy more dressers or handbag hangers or shoe racks or accessory bins either.
CULL.
General note about closets:
If they're full, you need to CULL, not move to a bigger place or get a storage unit.
You can do with a LOT less than you think.