Make gun ownership dependent on membership in a state regulated militia. Allow as many militias as people want to start, but they have to meet state set requirements for being well regulated, which must include background checks on all members as well as screening for dangerous mental illnesses.
Why is this important?
Gun violence is a result of the wrong people owning guns or of people without proper training and regard for weapons owning them. Making it a requirement of gun ownership to belong to a well regulated militia, as mentioned in the Second Amendment, would provide a means to ensure that neither of the above conditions occur.