There are actually two official alternate costume here. Hikari uses the Bride June outfit from ReLive (post #10747389), while Karen is dressing the Phantom Thief outfit from the Overture prequel manga (minus the mask)

Shoujo☆Kageki Revue Starlight Overture, chapter 06, page 31

The design is mostly the Revue outfit but with pants and longer tassel for the epaulette, but I love her