The rearranging of a whole's parts and their relations. Restructuring changes what is possible without changing what is there.
Latin structura (a building, a fitting together), from struere (to pile up, build), with re- (again) prefixed; a rearranging of what was already built rather than a building from nothing.
A change made to how the house's own parts relate to one another, done without discarding what already stood — what becomes possible changes, not what is there.