Removing part of double storey extenstion

Hi hope I'm posting in the right place, I live in a old house which has years of extensions build on (4+ I think) we have no garden attached to the rear. Is it possible to remove part of previous double extenstion to create outside space as the house is too big for us as it stands now. Possibly one room around 4m x 4m. What I'm asking is is this possible to do and how much cost would be involved( average)????

Also is it totally ridiculous to do the work/time/cost ect just to have an outside space at the rear of house???

Thanks in advance, new to boards so hope I can get some info. 😄