Make a fabric hanging slot container hanger (double sided) for balance. Or hang on back of door on hooks. Or you could make a display of them in the room maybe.
Shelf above the rod and add bins, shelving, or something to stack.
I actually use a narrow hanging fabric shoe rack to hold mine. It works great! HERE IS ONE that would work wonderfully.
I use a clear plastic bin, we refer to it as a "sweater" size as ithe is a good size to hold a few folded sweaters . It sets on the shelf above the rod.
I've limited myself to whatever number of purses will fit in the bin. When I buy a purse and don't have room in the bin for all I'm not currently using, I have to donate one or more so my favorites fit the bin.
A pretty basket would work, too.
You could put hooks on the back of the door to hang the purses from.