Extension on Townhouse

I assume the TH is 20' wide? Check to see if you can go out 10' - you have to leave X amount of the yard uncovered - unless you're doing a "greenhouse".

And, cost will depend a lot on access. If you're digging a proper foundation, how is the equipment going to get to the backyard? Are the construction workers going to have to dig & carry out each bucket load?

And what kind of extension? Are you going to provide heating & electricals & mechanicals? Windows/sliding doors? Roof material?

I know people who have done this work very cheaply (< 50k) but they were able to spec out & design the project themselves...