We derive the crossing matrix for scattering ${X}_{n}+{X}_{n}\ensuremath{\rightarrow}{X}_{n}+{X}_{n}$ of a multiplet of scalar mesons ${X}_{n}$ which transform according to the regular representation of $S{U}_{n}$, for all $n$. For $n=3$, or octet symmetry, in the limit of neglecting inelastic coupled channels we find that, if the ${J}^{P}={1}^{\ensuremath{-}}{8}^{\ensuremath{'}}$ channel resonates, so also should the other two ${1}^{\ensuremath{-}}$ channels 10 and $\overline{1}\overline{0}$. These decuplets resonate at essentially the same mass as the 8\ensuremath{'}, barring what are probably small corrections from crossed ${0}^{+}$ channels 8 and 27. Similarly, for general $n$, all ${J}^{P}={1}^{\ensuremath{-}}$ channels should resonate together. Application of the Gell-Mann and Okubo mass-splitting formula to the degenerate 8\ensuremath{'}, 10, and $\overline{1}\overline{0}$ leaves the 10 and $\overline{1}\overline{0}$ in energy regions which have been explored in experiments, at least if one assumes the 725-MeV ($K\ensuremath{\pi}$) resonance is a member of the decuplet. However, effects from coupled inelastic channels such as ${X}_{n}+{V}_{n}\ensuremath{\rightarrow}{X}_{n}+{V}_{n}$ (${V}_{n}$ is ${J}^{P}={1}^{\ensuremath{-}}$ multiplet) may remove the mass degeneracy in the limit before symmetry-breaking effects are introduced. The crossing relations for $n=3$ and ${V}_{3}={8}^{\ensuremath{'}}, 10, \overline{1}\overline{0}$ are examined and shown to be consistent with this explanation. For $n=3$, the ${X}_{3}+{X}_{3}\ensuremath{\rightarrow}{X}_{3}+{X}_{3}$ crossing relations favor a pseudoscalar, rather than a scalar octet ${X}_{3}$.