Customisable Characters/Objects

This is not exactly a coding question, but I'm sure a lot of people here know the answer so would be able to help me

My question is, how would one go about creating characters they can customise in terms of changing clothes, accessories, appearance, etc? Do you give the item the same rig as the character and just instantiate them on top of each other, or is there some other way to combine them without wasting as much resources?

There are obviously different ways of going about this, but I thought I'd ask to community to find the most effective or industry standard way of going about this.

Thanks in advance