Really good interview by Bob Binnie (Great fella) with Keith Delaplane on the effects of polyandry. Turns out if you can get more drones from a different line it helps improve population and reduces mite load. At least thats what Delaplanes research shows.
If you dont have the AI rig you can temporarily create this by mixing frames amongst your hive. I may try this in one yard to see if there is the intended outcomes.