Can you dig out a lower basement in a semi-detached house?

Yes. There are two ways to do it.

The first is to "curb" - that is, to build out a concrete curb the same width as the depth you want to drop. Example: if you want to add 12 inches to your basement height, you then have to build a solid concrete curb that comes out from your wall 12 inches, then drops 12 inches.

The second way to do it is to "underpin".

google both - "curbing basement" and "underpinning basement" for an explanation of how these things are done.

Either way - you will need the services of an engineer, a building permit and likely permission from your neighbours.

Good luck.