To reduce to resolving Cohen–Macaulay singularities, Faltings initiated the program of "Macaulayfying" a given Noetherian scheme X. Under various assumptions Faltings, Brodmann, and Kawasaki built the sought Cohen–Macaulay modifications without preserving the locus where X is already Cohen–Macaulay. We will discuss an approach that overcomes this difficulty and hence completes Faltings' program.