I believe Wheaten refers to the coloration, or plumage of a single Ameracauna bird. Ameracauna is the breed, so if there is any other breed introduced, you have a mutt or mongrel known as an Easter Egger. You will notice my profile picture. I was told that my Roo (RIP Wyatt) was a purebred Ameracauna. Well, simpleton and beginner that I am, I didn't know better until the kind knowledgeable folks on BYC informed me that his coloration was not true to the Ameracauna breed standards. This meant that my big boy was not an Ameracauna but an Easter Egger. There must have been some impurity in his past, even a couple generations ago that caused his plumage to fail him from showdom.
So, in order to get the various Wheatens such as Blue Wheaten, or Red, you mix Ameracauna colors, not other breeds with Ameracaunas.