Line the bottom of a large baking dish with the chicken breasts. Scatter Cheddar and Swiss cheese over top. Flake the tuna and salmon and layer evenly over the cheese. Mix whipping cream with the 4 beaten eggs in a bowl; pour over top of the dish.
Mix the feta, mozzarella and ricotta cheeses in a bowl; spread over the fish. Mix the cream cheese, 2 beaten eggs, and bread crumbs in a bowl; spread evenly over top of the cheese. Evenly arrange small pieces of butter over entire dish. Cover with aluminum foil.
Bake in preheated oven for 1 1/2 hours, or until heated through and golden brown on top.