  We investigate solutions of the classical Einstein or supergravity equations
that solve any set of quantum corrected Einstein equations in which the
Einstein tensor plus a multiple of the metric is equated to a symmetric
conserved tensor $T_{\mu \nu}$ constructed from sums of terms the involving
contractions of the metric and powers of arbitrary covariant derivatives of the
curvature tensor. A classical solution, such as an Einstein metric, is called
{\it universal} if, when evaluated on that Einstein metric, $T_{\mu \nu}$ is a
multiple of the metric. A Ricci flat classical solution is called {\it strongly
universal} if, when evaluated on that Ricci flat metric, $T_{\mu \nu}$
vanishes. It is well known that pp-waves in four spacetime dimensions are
strongly universal. We focus attention on a natural generalisation; Einstein
metrics with holonomy ${\rm Sim} (n-2)$ in which all scalar invariants are zero
or constant. In four dimensions we demonstrate that the generalised
Ghanam-Thompson metric is weakly universal and that the Goldberg-Kerr metric is
strongly universal; indeed, we show that universality extends to all
4-dimensional ${\rm Sim}(2)$ Einstein metrics. We also discuss generalizations
to higher dimensions.
