Well, considering that I don't support most laws or regulations in general (and more specifically the way in which most laws/regulations are enforced), regardless of the gun issue; I'd have to say no to supporting new firearms restrictions.
While the supposed goal of those restrictions might sound good to some, they wouldn't actually accomplish
said goal; which in this case is the prevention or at least reduction of these mass killings. The all too easy case-in-point, look at how well anti-drug laws have worked.
And since drinking and driving is illegal, we all know that there are no alcohol related traffic deaths..........
Gun restrictions don't prevent gun related violence, any more than drug restrictions prevent drug related violence. If you want results, work on making people smarter (and no I do not mean educated). Better yet, try to instill a sense of morality in them......good luck with that. It would be awesome if we had no "need" for guns from a self defense perspective, but while we're at it we might as well be looking out for unicorns and searching for pots of gold at the end of rainbows.
Meanwhile in the real world, there will still be robberies, murders, rapes, carjackings, bombings............and yes there will still be the kinds of mass shootings we've been seeing too often in the news recently. Make it 100% illegal to purchase a firearm and all of those things are still going to happen. It's not pretty, but the truth rarely is.