Slab-on-ground foundations are repaired by lifting low areas
They are not repaired by forcing high areas down. Foundation repair usually means making the slab surface more level. Most homeowners are mostly concerned about drywall cracks, brick veneer cracks, and door issues. They are doubly concerned if after making repairs to the house the same problems return. How level the foundation is is a minor issue unless it is noticeable. Most people have a hard time perceiving a floor slope of less than 1%.
Lifting a slab-on-ground foundation has to be coordinated
Usually, the person in charge will stay inside the house and will give instructions to the other crew members. Everyone will have a walkie-talkie. Each lift is somewhere around a quarter-inch to a half-inch. The person in charge will count down and then several people will lift the specified amount. After the lift, the inside and outside will be examined for any new distress or damage. If there is no new damage, then the lifting can continue. Section by section by section will be lifted as long as the house tolerates the lifting process.
If the house starts to react with distress or damage, then the owner and the contractor jointly decide how and whether to proceed.
The more you lift the more risk you take
The more you lift, the more of the slab becomes elevated. This is always a potential problem. As more of the slab is lifted, structural damage becomes more likely. Even if there appears to be no issue, it can show up as late as a couple years later.
Why a stiffer foundation is a better foundation despite being less level
All slab-on-ground foundations react to expansive supporting soil by bending or tilting. If a foundation was super flexible it would bend but not tilt. Conversely, if the foundation was super-rigid, it would tilt but not bend. Remember, foundation bending results in distress, damage or both to the house. Tilt does not have an adverse effect on the house.
Having pointed this out, it is stiff foundations that tilt and create large elevation differences.