There is no obvious answer to this question. Here are some things to keep in mind:
If you underpin the entire perimeter, there are two significant risks
First, if the contractor wants the slab surface to be more level, the perimeter grade beams will be lifted off the supporting soil underneath the grade beams. This may make the slab surface more level, but it will also create a situation where moisture can more easily penetrate to the supporting soil under the perimeter grade beams.
Second, if the slab foundation is to be supported but not lifted, the perimeter is likely to wind up uplifted off the supporting soil the next time we have a drought. The perimeter piles are likely to prevent the perimeter grade beam from floating down with the supporting soil.
If you underpin only a portion of the perimeter
Now the portion that is underpinned is or will become, an elevated structure. The portion that is not underpinned will continue as a ground-supported structure. There is close to a 100% chance that the two areas, the elevated portion, and the ground-supported portion will react differently to soil movement.
Thus, rather than making the foundation more stable, it may be less stable or the differential movement between the two areas create new distress or damage issues.
If you choose to not underpin the interior
Underpinning the interior of the slab foundation is not common. Most homeowners choose not to go this route due in large part to the cost. If a homeowner chooses to underpin the interior stiffening beams, they have a choice between jackhammering the slab from inside their home or installing the underpinning from tunnels underneath the slab. So the choice is between tearing up your home or spending gobs of money on tunnels beneath your home.
Underpinning the interior of a slab foundation is sometimes recommended if the perimeter is to be lifted higher than normal. Another reason is when the perimeter is lifted and later a drought occurs. The perimeter is held up by the perimeter underpinning and the interior settles downward. Underpinning the interior under these circumstances probably occurs around a third of the time.