Hiding menu options on a masked piece from all players

Hi, I’m making a module for Flash Point: Fire Rescue for personal use and I’ll post it publicly if I get permission from the publisher. I’m having trouble with the masking feature. In the game are POI tokens that are secret from the players, who are all working together. Some of these tokens have the option to apply a layer to them, but unfortunately, due to how masking works, the player who drew them from the POI deck can see that option (and probably more options I’ll end up adding) and determine what kind of POI it is. Is there any way to prevent everyone, including the masking player, from seeing the other menu options on a masked piece? I can add all options to all POI tokens if necessary, but that seems like a kludgy solution and I’m hoping there’s a better one.

Thanks, Arona.