As someone once told me about remodeling (and our experience proved) with money you can do anything. We had the same problem. Concrete back stairs were parallel to the existing foundation, and right where we wanted our new space. So we dug out for a new foundation and created stairs and basement entrance on the other side of the house. It all worked fine.

Our original concrete outside stairs are now inside our house thanks to a previous owner. Our stairs went directly out from the original basement back door, not sideways like yours. Our stairs are now inside our backdoor and are the final run of stairs to our basement.

An addition can definitely happen. How you handle the stairs depends on how large an addition you hope for.

I'd be more concerned about what new outside finish you'll have to coordinate with the original brick. Odds are very high you won't be able to match the brick.