Need a little clarity on what you mean by "adding a basement".

Currently, there is about 200 sq ft of basement. I think the foundation is limestone. We would like to increase that to approx. 1,000 sq ft to accomodate a finished family room, 2 bedrooms and bathroom. We've considered moving to gain the space, but there are other aspects of the house that we like (location, floor-plan, kitchen, etc.)

I appreciate any input you could offer! Thanks!

Sorry, still confused. I am guessing that you want to dig away the dirt from the remainder of your house to increase the size of the basement and there is a wall that will have to be removed.

Yes, we want to expand the size of the basement. I have heard of people who 'jacked up' their house and had a new basement dug and poured, and then the house is placed back on the new basement. I was wondering how costly of a process this might be and drawbacks of the process.

Sorry for the delay.
Without actually seeing the scope of the job it is difficult to give you an exact price. The area you live in is also a determining factor. This is a very labor intensive job since the dirt would have to be hauled out in some manner. A ballpark figure would be in the $15K to $30K dollar area. Cost effective?
I would think that you would get better value for your money by having an addition with a basement installed. You could make a major savings by installing the framework and then complete it with sweat equity- probably a 50% savings. As mentioned before, the price I quoted is not bible. A few bids would better verify all the costs. I hope this answers your questions. You can reach me at drhome@shoppittsburgh.net if you have any further questions. Don't forget to measure your values versus the money....

Thanks for your input! I am contacting some firms to get some bids and decide from there.