I am looking at a house with a 6.5' basement ceiling height. What is a ballpark figure for digging out a 15'x 40' basement? It does have access to the outside through a bulkhead.
I don't know the answer to your question - & don't know the age of your building - but are you sure the footings are deep enough to allow for a lower floor? Or do you even have footings? I'm in an urban area in the mid-Atlantic, & 19th century townhouses around here didn't have footings - they laid the first brick course directly on clay about 8-12" below the intended basement floor.
Its a fairly common thing to dig out basements here, and what is often done is to not dig out the entire width or length of the building but rather leave a perimeter of undisturbed (relatively, I guess) soil around the foundation and dig out the middle Then it ends up having a shelf of sorts around the whole thing that is concreted.
You are right, though, it may not be possible or advisable depending upon the situation. I know someone who has two adjoined houses and they dug out one basement and essentially filled the other one in. Two adjacent foundations, two different scenarios. They couldn't give me an idea about the price since it was bundled into a whole gut renovation.