Practically, not much. You'd either want to decrease the amount of vengeful anger or decrease access to firearms. The emotions [and thought-patterns, as emotions themselves don't recommend complex action] that would motivate someone to commit a mass-shooting -- I don't know what to reason about that. I don't think the actions are ever rational, and it has the problem of being rare. You could surmise causes, but it would be hard to test.
Reducing the saturation of firearms in the US is...political. Something to do with the wild west history, fear of government and criminals -- general mistrust, I guess, and the US military and police as major powers. I don't quite understand all of it, but it mixes together to say the more weapons per person, the better for our nation.