Personally, I think that would cause big problems if something does happen accident wise and then you want to collect from the insurance company. Insurance companies, like any business out there, are trying to make money. If they can find a loop hole to not pay, they will. Finding out that a car is insured by another company would be a nice big loop hole to say "nope, it's the responsibility of the other company to pay" and volley you back and forth with neither wanting to own up to the responsibility of giving them the payout they deserve. There must be a way to adjust one of the insurances policies to cover both parties without having to worry about the vehicle being double insured.