Give choice about the modifiers : you can choose which and how many you want ( from 0 to 4) and save a several configurations.
As incentive, each modifier increases substantially drops rate both world and dedicated.
Clearly tag weapon to indicate what mayhem level they are.
Balance some modifiers add a few others. Add a fifth category: special event will include things like Cartel reinforcements.
Add mayhem scaling for nova, spike, grenades and relics.
Add automatically a modifier that substantially increase melee, action skill damage, pets, with a value in proportion with mayhem so they can still be competitive.