It is decently common, though unlikely the majority. This is dependent on the school, and I am not sure that there is actually a list of all the schools in either category.
You can generally decipher this by either reading the school's admissions page or just guessing based on their philosophy. Some schools are very adamant about their mission and weight their secondaries and letters heavily, and if that is the philosophy of the school then you can be quite sure they do. Other schools (like my own, historically) would do things like invite solely based on your demographic information (GPA/MCAT/Residency) before digging into primaries, secondaries, and letters, which are more subjective.
As for whether you'd have 4 additional II if you had a bad letter, I doubt it. If there is a red flag in your letters you would probably be getting torched by most everyone.