  In this paper we show that for any fusion $\mathcal{B}$ of an association
scheme $\mathcal{A}$, the generalized Hamming scheme $H(n,\mathcal{B})$ is a
nontrivial fusion of $H(n,\mathcal{A})$. We analyze the case where
$\mathcal{A}$ is the association scheme on a strongly-regular graph, and
determine the parameters of all strongly-regular graphs for which the
generalized Hamming scheme, $H(2,\mathcal{A})$, has extra fusions, in addition
to the one arising from the trivial fusion of $\mathcal{A}$.
