  Given any group $G$, the normalizer $\mathrm{Hol}(G)$ of the subgroup of left
translations in the group of all permutations on $G$ is called the holomorph,
and the normalizer $\mathrm{NHol}(G)$ of $\mathrm{Hol}(G)$ in turn is called
the multiple holomorph. The quotient $T(G) = \mathrm{NHol}(G)/\mathrm{Hol}(G)$
has been computed for various families of groups $G$ in the literature. In this
paper, we shall supplement the existing results by considering finite split
metacyclic $p$-groups $G $ with $p$ an odd prime. We are able to give a closed
formula for the order of $T(G)$ when $G$ satisfies some mild conditions. Our
work gives a new family of groups $G$ for which $T(G)$ is not a $2$-group.
