I think every gun that is sold should come with a standard capacity magazine for that type of gun. Say, 8 round for a semiautomatic handgun, as an example. If you want a higher-capacity magazine you should have a separate background check and go through an FBI or ATF permit process wherein the magazine is registered. This way they can identify people trying to acquire large numbers of high-capacity mags. Could catch that red flag. Same could be done for buying large amounts of ammo.
For my 9mm I have about 6 magazines. 2 standard capacity (I think mine are 13), and a few military spec that hold 15, and 2 extended mags that hold 19. But when I go shooting I almost always just use the lower capacity mags because it doesn't extend the size of the gun by extending out the handle. In the last, oh say decade, I've shot from the high-capacity mags maybe 6 or 8 times total. And this was even when I was participating in competition shooting. There is almost never a reason for an extended mag on a handgun. And very few for extended mags on rifles. The only rifle I have with an extended mag is essentially the sport version of the AR-15, a semiautomatic .223 I use for varmint, but that is just because often you are taking a lot of shots after another when you kick up a bunch of jackrabbits or something. Even then it holds 15 rounds I think, and my basic gun holds 6. But the actual "need" is pretty minor.
The one monkey-wrench in all this is, like the Columbine killers, they can have other people acquire their weapons. And it still does nothing for places like gun shows or private sales or illegally acquired weapons.
This is an insanely tough nut to crack. So many guns are already out there. Almost anything short of a full-scale military level confiscation of all guns won't do much to curtail the problem.