Underpinning is what it's called to strengthen a foundation.

Just inspected a new house that already has shown settling of its concrete block foundation. It may just be a drainage issue: the whole rear of the 3-unit structure drains to the side that is settling so redirecting that water may fix it. If not, the footing for the wall needs additional support. The new hardware demonstrated in the above video seems promising. Another method is called the push pier system, as demonstrated below.

#concrete