Regardless of whether or not you can build more than one AWC (you can't), you don't actually need to increase your chances, because the chance of a bonus skill is guaranteed*.
The way the game works, when the AWC is built (for existing soldiers) or when a rookie promotes to squaddie, a single random bonus perk is assigned, as is a rank (from Corporal through Colonel). Whenever the soldier reaches that level, they get the bonus perk.
* The exception happens in that the AWC only checks for exactly that rank, so if, by the time you complete the AWC, one of your soldiers is a Captain, and their bonus ability rolls at the Sergeant rank, they will never unlock it, because the AWC only checks their current rank each time they promote. (There is a mod that fixes this, however)