I did an addition on my home 8 years ago. We put on a 2nd story on a one story house. I used cash for the 2nd story addition, then a home equity loan for the first floor redesign.
For you, this may require some back and forth between communicating with builders (and architects), communicating with banks and communicating with realtors/house assessors.
Regarding construction, concrete work is extremely expensive. We did not need to do any concrete work. We took off the roof and put on a 2nd story. Had we gone back or out to the sides of the house, the excavation and the concrete work would have added considerable cost. Possibly 25% or more (I don't have exact figures).
This will take some research on your part. Have an idea of what kind of addition you want to do, then talk with builders to get a sense of that cost, then talk to an appraiser to see what that will do to your house, and talk with a banker to see what's feasible.
Patience will be required. Best wishes. Living through construction is a whole separate topic =)