I assumes this is an old house?
Are you sure you guys really want to do this?
Afterall, changing a 6' height room to a 7' height is still, well, small.

Look at it from the logistical aspect - just demo-ing the 5" thk concrete slab and repouring a new 18X27 area are already monumental. Other issues to consider are structure, substrate, existing piping infrastucture, refinishing the wall,/base & flooring rtc.

Of course many of these issues are easier to resolve if it's just a dirt floor - which I have seem in older houses.

You are going to need an engieneering review to make sure you can dig without disturbing footers.
Typically you can go no lower than the bottom of a footer without providing some means to prevent the footer from moving into the hole.
Try a structural or geotechnical, and you may need both.