I have had the same problem to deal with on a customers house.The existing posts under the main carrying beam where failing or had been altered or just not there. I was able to come in with screw jacks poistioned stretegically all along the old beam and lifted each jack very slowly and i repeat very slowly over a period of time.Once we got the beam to where we were satisfied, (and that took some time, and problems will arise along the way)we were able to sister a triple glue lam directly up against the old beam making sure the floor joist had enough distance overlapping the new beam.Then new beefy footings were excavated below the existing concrete floor and allowed to cure, the floor was patched and allowed to cure,and, new steel lolly columns where installed at the proper distances before the jacks where removed and the new beam started carrying the load.Did it go trouble free no.....every situation is different so proceed slow and plan on it taking some time.Above all your eyes and ears have to be very alert as to what is happening in the over all picture.