Instead of gaining Honor when you Proclaim, draw cards equal to half the Honor you would have gained, rounded up.
Can I play more than one copy in response to a single proclaim?
Casting Aside Honor
A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
Can I play more than one copy in response to a single proclaim?
You can indeed use more than one copy of Casting Aside Honor per action.
That said, each one creates a delayed substitution effect, and when those go to trigger only the first one will net you cards, as there will no longer be an Honor gain to substitute with card draw when the subsequent ones go to resolve.