bnard, there are many ways to underpin a structure besides jet grouting. A few of the ones that I have seen used: hand work (already noted), augered cast in place piles, screw anchors, pin piles (jacked into place), and drilled piers (installed from the outside and a needle beam placed under the corner).
Talk with the geotechnical engineer for the project, he/she should be able to give you a shorter list customized for the project.