Yes, in addition to the currently existing ones, there should be restrictions that thoroughly check your background, for things like crimes, records of "craziness", and etc., and have you go for tests to determine if you have any traits that fall under "craziness that induces a shooting", or for any signs that you are mentally ill or psychologically crazy, which would indicate that you should not be trusted with a gun. These restrictions should be added to the already existing ones.