  The classical double copy idea relates some solutions of Einstein's theory
with those of gauge and scalar field theories. We study the Kerr-Schild-Kundt
(KSK) class of metrics in $d$-dimensions in the context of possible new
examples of this idea. We first show that it is possible to solve the
Einstein-Yang-Mills system exactly using the solutions of a Klein-Gordon type
scalar equation when the metric is the $pp$-wave metric which is the simplest
member of the KSK class. In the more general KSK class, the solutions of a
scalar equation also solve the Yang-Mills, Maxwell and
Einstein-Yang-Mills-Maxwell equations exactly albeit with a null fluid source.
Hence in the general KSK class, the double copy correspondence is not as
clean-cut as in the case of the $pp$-wave. In our treatment all the gauge
fields couple to dynamical gravity, and are not treated as test fields. We also
briefly study G\"{o}del type metrics along the same lines.
