I suspect that effective laws to stop mass shootings, and avoiding infringement of the 2nd Amendment are mutually exclusive. Some things could be done, however. Examples:
- Universal background checks could make it more difficult for shady people to possess firearms. Would it reduce mass shootings? No way to find out until you try it.
- Take a look at how other nations handle it. Swiss law requires firearm owners to not only register their firearms, but also firearm components, and ammunition...each round. Even with these strict regulations, the Swiss have a gun ownership rate that is fairly substantial...about half of the US rate. Does Swiss law violate the 2nd Amendment? I don't know, but they have a firearm related death rate that is about 1/3 of the US rate.
- In vast portions of our society, technology has made life better. Why not introduce technology solutions into firearm products? The idea of smart guns is intriguing, and certainly doesn't infringe the 2nd Amendment. I chuckled several months ago when I heard somebody claim that the technology doesn't work. He had never seen a smart gun, never held one in his hand, never fired one, and even admitted he really didn't know much about how it operated. But he was absolutely certain "it didn't work" and that "a 10 year-old could modify it to a non-smart gun in 20 minutes".
- If our society was serious about stopping mass shootings, it can be done. In 1996, Australia instituted draconian restrictions on firearm ownership, and it worked. There have been no mass shooting in Australia since. Of course, they don't have a 2nd Amendment.
So maybe the solution comes down to a very very fundamental choice. We either overturn the 2nd Amendment and eliminate the right to bear arms, or we overturn the 5th amendment and eliminate the right to life. Either one would solve the problem and we can stop arguing about it.