I've had a few ideas that might help, but certainly not stop, the flow of guns to criminals; but those involve things like gun registries, ammo registries, improving serial numbers (so they can't be obliterated), and complete bans on resale of guns other than back to a licensed firearm dealer. But I've pretty much never heard a gun enthusiast agree (some gun _owners_ have agreed, but mere owners aren't the ones that need convincing about reasonable gun control).
None of that would stop mass shootings.
In fact, I don't think we can pass *anything* consistent with the 2nd Amd. that will stop or even reasonably cut down on mass shootings. Ditto for the rest of gun violence in this country. There are just so many guns out there.
We'd need to repeal the 2nd, confiscate the myriad guns out there, pass a new much more limited 2nd, and start all over. Not happening. That's less likely than building a wall, forcing Mexico to pay for it, deporting all the illegals, and actually keeping them all out. HAH!
Basically, either Americans are extremely violent evil people as compared to the rest of the world, or having the most guns per capita means you have the most gun violence per capita (not including broken states like El Salvador).
The guns aren't going anywhere. So, as tragic and frustrating as it is, we're going to have to get used to the idea that if you live in America, you're far more likely to be gunned down than in any other "civilized" nation.