Reading an old Literary Digest magazine for 1915 (I am slightly behind in my reading), I saw an add for the KisselKar, a four-door with a removable hard top.
"The all-year car, a Kissel idea, supplies for the first time the comfortable and continuous every-day use of one car the year 'round without sacrificing appearance or refinement. A closed car in winter-- a touring car in summer."

Some sports cars have mechanical hard tops (BMW for one), and several in the past have had removable hard tops, but the Kissel is the only one I have found that has a top for a four-door sedan.
"Tops can be quickly attached and detached in your own garage as often as weather conditions dictate."

Perhaps car buffs can tell me of others.