It is almost certain that you will have to modify the foundation to make it deeper too - and that is MAJOR structural work.
You need a civil/geotechnical engineering firm with experience in foundation rehab and putting in basements under existing homes to design the process and prepare and seal the plans and specifications, which you will need before you can get a building permit for this. They will also be able to help you select either a foundation excavation or a house moving and jacking company to do the actual work for you.
The engineer can also help you with a cost estimate - because I think you will be surprised how much this is going to cost. I have designed or managed quite a few such jobs, from highrise buildings to homes, and even the smallest houses of about 600SF footprint ran at least $15,000, and generally house basement excavations run more like $25-40,000 unless the foundation was originally designed for it but for some reason the basement was never put in, which is VERY rare except in very deep frost areas were footings are occasionally deep enough to allow a basement to be dug without deepening them. I worked on a couple back east that ran about $100,000 each because they were old 2-story brick buildings, which are very sensitive to differential movements - probably like yours.
A couple of other factors to consider is that in doing this you are likely to get at least some minor drywall cracking and door and window jamming, and be sure the contractor is insured and bonded to the hilt and for the potential rebuild value of the house, not just the job cost, because a major mistake can turn your house into a teardown. Not common, but the less experienced the contractor the more likely he is to do something dramatically wrong, and at the same time the smaller and less experienced contractors generally have lower coverages so your risks is compounded in two ways. With a row home you have the added risk of damaging adjacent units.
One thing to consider cost wise before you go ahead - I have worked a couple of jobs where it turned out cheaper and far safer to scrap the digging in a basement idea and put in an addition with same footprint instead. However, looking back I see you are in a row home, so that is likely not going to work. However, being in a row home, especially if on the Potomac flats south or east of the capital area, the soil conditions are generally the pits once you get off the Georgetown heights, so putting a basement under a rowhome without disturbing the other ones is VERY difficult and pricey - I would be surprised if you could do it for less than $100,000.
One other factor is utilities - one of the first things to do is check depth to any utilities like sewer lines, the Metro, etc - if you are over one of those that could well put your project totally out of the frame of reality.
You asked for a recommendation - one who specializes in this type of work that I would recommend, though your job might well be too small size for them - but they might be able to give you an engineer and contractor recommendation if so. Company name is Schnabel Foundation Company in Sterling Va and Bethesda, MD in your area - website www.schnabel.com. They could handle both the engineering and construction.