That shouldn't be a problem if you don't overdo it, otherwise the beurrage might break and interfere with folds and puffing. A simpler way might be just sprinkle your flavor on the finished dough triangles when you make the croissants, then roll it up (like cinnamon rolls). Especially parmesan (or any cheese) might mess something up if you mix it into the butter.
That shouldn't be a problem if you don't overdo it, otherwise the beurrage might break and interfere with folds and puffing.
A simpler way might be just sprinkle your flavor on the finished dough triangles when you make the croissants, then roll it up (like cinnamon rolls). Especially parmesan (or any cheese) might mess something up if you mix it into the butter.