This came up at the prime tournament today.
My opponent's Biggs (at distance 1-2 of Jan Ors, both with a usable brace token) was on the receiving end of 3 damage from my squadron. My opponent argued that he could use Jan's brace to reduce the damage to 2 and then use Biggs' brace to reduce it to 1. He may have also argued that being able to move the damage with Biggs had some impact on the result, but I can't remember exactly what that was.
My understanding is that you can only use one brace per attack and, even if you could, the wording of brace would only apply once. Am I mistaken?