I know you didn't ask me, but I often rush in where lesser fools fear to tread.
I don't see why, in principle, a "Not Protestant" caucus couldn't be declared.
But, WOW it would be exciting to see who thought they had a place in that caucus -- and who agreed or disagreed with them.
As just one for instance, until not too long ago the official name of the Episcopalians was The Protestant Episcopal Church in the United States of America, and certainly in Fielding's time the C of E considered itself Protestant.
The Protestant Reformation really did involve a very few “denominations.” Those were the reformed and the lutheran and the presbyterians.
The Anglicans sort of got involved, but not for reformationist reasons. They broke away because of kings and personal politics driving kings.
Non-protestant groups today would definitely include: all charismatic and pentecostal groups, Mormons, many baptistic groups, the orthodox of all stripes, all restorationist groups, and the “lets-hang-out-a-shingle” groups with weird names.
I’m not trying to be argumentative. It’s just that the protestant reformation actually meant something about its relationship to breaking away from the Catholic Church.