I live in a house built in the 1920s. Had a (maybe) 6' basement made out of a mix of brick, cinderblocks and clay. Water down there every time it rained. I hired a structural engineering company to design a plan to dig down far enough to give myself 8' finished ceilings for my home theater. I had 2 choices - underpinning so I could dig right up to the foundation walls (basically use the full footprint of the house) or come in from the walls as far as I wanted to dig down and leave a ledge all the way around the perimeter. I went with the second option because underpinning was like 5x as expensive. The ledge ended up working out just fine because I left all of my utilities against the walls and then built interior walls with closet doors/fake countertops to hide the ledge. Looks like the whole room has 8' ceilings - you can't tell. Anyway, this was a very very complex and costly project.

Hire a structural engineer. Do not attempt this yourself.

EDIT: Here's a pic of the "ledge" and how we had to get creative to dress it up. The drawers work and the doors open but the lower cabinets are mostly filled with concrete. There is about 8" of space on top of the ledge and under the drawer for storage but from looking at it you would never know.

And here is a pic of my equipment closet, which has the ledge inside but it's a regular door that goes to the floor.