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Starting in the Legion pre-expansion patch, you can access the new transmog system.
Go to a transmog NPC in major cities and click on them to open up the transmog window.
The transmog window is similar to the existing window with a paperdoll and slots you click on to apply transmog. However, it is greatly expanded with your wardrobe collection on the right-hand side.
The transmog window also now includes the option to save outfits.
You must be by an NPC to transmog and change your appearances, but you can browse your collection anywhere just by opening up your tab.