As far as I can see, when you extrude a surface, it is actually moved, not copied. As a result the original surface ( the “base” ) is lost and if you need it you have to re-create it. So my question is : can you extrude a surface while keeping the original ?
Although Sanctuary has given you a way to do this you haven’t told us why you want to have this geometry. I for one see absolutely no use for this and can think of any number of serious problems down the line when you do this. Just a tip!