I agree with the other answers. Here is what you need to know.
1. Legal ceiling height in the basement needs to be 7'-6" above the new slab. (finished)
2. You need to know the Zoning limits of your building. (Lot Area vs. Building Area)
3. In order for the NEW basement area to NOT count against you, it must be more than half below grade. (Height from Sidewalk at property line to top of first floor finished vs. height of basement slab to height of first floor finished)
4. The depth of the existing foundation should be BELOW the new slab height.
5. If NOT then you will have to underpin the foundations which will throw the 20K OUT OF THE WINDOW.
6. Any plumbing will need to be lowered and you may end up needing an overhead ejector pump.
Feel free to contact me if you have any questions. I have worked on these types of projects before and as an Architect I can help.
Also concerns with water and drainage.
Structure is your main initial concern; for long term viability your next big concern is waterproofing. I have completed many of these types of projects and I have purchased bank owned homes where the job was done incorrectly and I had to fix bad work.
After you answer the questions above I can give a better idea of what this type of project might cost.
RpV Realty and Development
I have worked with him in the past when buildings I have inspected needed a structural engineer.