Yes, the DLC adds side missions found in special distortions, which unlock as you progress through the DLC. You may need to reroll your missions at a bench to make it update. Each mission involves defeating a character and their sidekick in a double battle, which then unlocks new customization options.
Each character will give you a replica of various items from their own outfit, and defeating them a second time later (a new mission will unlock after more progression) unlocks new colorways for those items. You also unlock the ability to copy their hairstyle in any color.
This applies to the following characters:
- Canari
- Ivor
- Corbeau
- Jacinthe
- Grisham
Unfortunately, you can't get the sidekicks' outfits, which means you can't copy Tarragon, Gwynn, Phillipe, Lebanne, or Griselle.