[Big Dave]

Hot rodders have done crazier stuff than this but with uni-body construction it would require the services of a very talented and well equipped body shop.

You could probably achieve getting the car down to 60% of initial width. A lot of it depends on where your engine sits. If it sits ahead of or behind the fron wheels you are good to go. If it sits between the wheels you are stymied.

Maybe a better and certainly still radical move would be to chop the top, if you are short enough to live with a low top sill.