It's been tried.
Every time I've seen it tried, some Catholic crashes it and pitches such a fit that the caucus label usually ends up being removed.
Prot caucus doesn't seem to be as protected as the Catholic caucus are, for all the whining about favoritism of the Protestants by the Catholics.
Personally, I don’t want a Caucus area of my own.
Our strategy is well documented.
Our purpose is public and our message is for everyone.