Hi Kevin, and you are welcome. I am by no means an expert, but I've simply learned most of this by doing.
I recently looked at a beautiful turn of the century house in NW Portland, much in need of renovation, and with exactly the same problem....the basement floor needs to be lowered. With the new primary residence capital gains tax exclusion, we are seriously considering this house.
The research I have done so far says that you can go down to your footings, but cannot dig down deeper than a line drawn out at 45 degrees from the top edge of the footing. The other considerations are how deep your main waste pipe goes. My plummer friend says you should have at least 2 to 3 inches of fill between the top of this pipe and the bottom of your slab. This should ensure the pipe has room for expansion/contraction. To determine how much room I have to the main drain pipe and the top of the footings, I chucked a long 3/8" rod into my 1/2" drill and ran it down into the dirt first along side the 4" drain until I could 'feel' it turn horizontally; then I did the same along side the poured wall until I could 'feel' the top of the footing. Fortunately, I can dig down a little over 2 feet.
My plan is to go down the most I can, giving me the deepest basement I can get. I recently visited a friend in a new house with a 9.5 foot basement....wow.....it didn't feel like a basement at all.
Of course other factors you may have to plan are going to be digging and pouring new deep footings for lolly columns (the first thing you should do); extending stair stringers/building landings; extending furnace plenum; lowering windows and rebuilding and digging out any exterior basement doorways. A fairly sizable project, but something you should be able to take your time on and once finished......what a reward!!
Best wishes and please post back your challanges and progress.