Normal Macaulayfications Given any reduced excellent scheme $X$, there exists a Macaulayfication $\pi : Y \to X$.  In other words, there exists a proper birational map $\pi$ from a Cohen-Macaulay scheme $Y$ to $X$.  These exist by a result of Kawasaki.
Is it possible that we may also pick $Y$ to be normal?  I see no reason why this should be true from the construction (blowing up various systems of parameters).  Of course, when resolutions of singularities exist, this certainly solves the problem...
One might hope that the normalization of a Cohen-Macaulay scheme is Cohen-Macaulay, but I believe this is false (for example given a normal non-CM variety in characteristic zero, you should be able to generically project it to a hypersurface).
 A: Karl, I do not know the answer for your question. However, it is true that, after Kawasaki's result, it has had more papers concerning your question. The following paper, due to Peter Schenzel, is such as a point:
Schenzel, Peter. On birational Macaulayfications and Cohen-Macaulay canonical modules. J. Algebra 275 (2004), no. 2, 751--770.
Perhaps, I have to be more precise.
Background:
Let $(A,\mathfrak{m},\mathbb{K})$ be a local domain. We say that $A$ admits a birational Macaulayfication provided there is an extension ring $A\subseteq B\subseteq\mathbb{Q} (A)$ (where $\mathbb{Q} (A)$ denotes the fraction field of $A$) such that $B$ is a finitely generated Cohen-Macaulay $A$-module.
On the other hand, we say that $A$ is \emph{canonically Cohen-Macaulay} (From now on, CCM for the sake of brevity) if the top module of deficiencies $K_A$ (that is, the canonical module for $A$) is a Cohen-Macaulay module.
In this setup, the main result of Schenzel's paper says that a local domain $A$ which admits a dualizying complex (that is, $A$ must be the homomorphic image of a Gorenstein local ring because of Kawasaki-Sharp's theorem) admits a birational Macaulayfication if and only if $A$ is CCM.
A: The paper Macaulayfication preserving the CM locus (arXiv:1810.04493) by Kestutis Cesnavicius has the following abstract:

To reduce to resolving Cohen-Macaulay singularities, Faltings initiated the program of "Macaulayfying" a given Noetherian scheme $X$. For a wide class of $X$, Kawasaki built the sought Cohen-Macaulay modifications, with a crucial drawback that his blowups did not preserve the locus $\mathrm{CM}(X) \subset X$ where $X$ is already Cohen-Macaulay. We extend Kawasaki's methods to show that every quasi-excellent, Noetherian scheme $X$ has a Cohen-Macaulay $\widetilde{X}$ with a proper map $\widetilde{X} \rightarrow X$ that is an isomorphism over $\mathrm{CM}(X)$. This completes Faltings' program, reduces the conjectural resolution of singularities to the Cohen-Macaulay case, and implies that every proper, smooth scheme over a number field has a proper, flat, Cohen-Macaulay model over the ring of integers.

