Well, we know from Gotham Central that the Joker had a number of accurate Robin costumes run up for some plan or other he never got around to using.
Actually, I can picture Joker and Harley having their own little Bat-wardrobe with a complete set of Bat-clan costumes.. and every once in a while, when he's bored, one or other, or both, or a hapless innocent, will put random combinations on... and unspeakableness of one form or another will occur.