I have a super old home in a 4-corner layout. When we walk, there's quite a bit of bounce. You should see it when we play the Wii!
Each quadrant's span is about 14' - a few inches over. The joists are 2x8 (true size), 18" O.C. One end is nailed to a beam that rests on the foundation wall, the other is notched into the inside beams (center of the house). There's no ceiling down there and very little "cross bracing" - one in the center of each span. Oh, and there's no plywood subfloor. This house was built long before plywood was invented. I believe there are simply two layers of wood plan floor ... the "sub floor" layer and then the soft wood flooring above. Spilled drinks quickly make their way to the basement!
As a test, I added a 4x6 beam under the living room with two jacking stands. I only applied a little pressure - wasn't trying to jack it up, just support it. It's now rock solid.
My initial thought is that it would be preferable to NOT use adjustable stands, but rather some form of improved cross bracing or sistering LVL beams to the existing.
I read about Luxor's IBS2000, which looks really effective.
Does anyone have any suggestions?