Well, I just have a couple of things to say about this:

In the end I want to be able to know other Pieces of Clothing with the same Tag, in the same Outfit and of the same type.
All of these things are features of clothing which you could compare in instances to see if they are same or different.

with only one copy of the each object so I could edit it after creation.
I don't see a point in that. Most C++ objects are mutable anyway. If you are managing several outfits, then you would want to use separate instances of clothing anyway.