I have heard of car insurance policies that cover the driver (whatever vehicles he owns and happens to be driving at the time) but I've never had such a policy since I've never owned multiple cars. I would think a policy that covers the drone pilot and any drone he flies would be an easier policy to manage (calculate cost of providing the insurance). The premium would be based on the most expensive, highest performance, heaviest drone he owns but would cover all the others (less, expensive, lower performance, lighter, etc.). As the OP mentioned you can only fly one at a time.
I haven't researched insurance beyond the basic coverage you get with AMA membership (non-commercial use) which does cover the pilot regardless of the drone he/she is flying.