There is not such thing as “Classico Alfredo Sauce” There is Fettuccine Alfredo, which is jus a way of preparing pasta using butter and original Parmesan (Parmiggiano reggiano) cheese. No sauce at all. Nice dish but hardly “classico”as it was invented officially only in 1908.
Alfredo sauce is an American invention of a ready-made sauce allowing to imitate the original Fettuccine Alfredo. You can add any spices to it at will. Nothing shall make it worse that it already is.