Buyers walking into a Cadillac dealer in the near future could find an interesting thing on the car lot: nothing.

General Motors Co.’s luxury division has about three times as many U.S. stores as German luxury auto makers or Toyota Motor Co.’s Lexus, but sells only about half the volume. Short of steering around rigid state franchise laws and hammering out financial settlements to shutter stores, a plan is being hatched to convert a portion of Cadillac’s 925 stores into virtual dealerships that will be low on overhead and...