 Take a possible world which is truly described by a dynamical theory of space-time (i.e., described by general relativity and any likely successor to it). Now take a second possible world which differs from the first only with respect to a tiny change, on a millimeter scale as regards length, and on a milligram scale as regards mass. This involves altering spatio-temporal relations throughout the entire universe. Hence it’s a consequence of metrical essentialism that in the second possible world, all space-time points are non-identical to those in the first. But surely it’s implausible that such a small adjustment should add up to such a world-altering difference (thanks here to Jeremy Butterfield).