A mixing of near-threshold quarkonium-like resonances with heavy meson-antimeson pairs results in an enhancement of heavy quark spin symmetry breaking, since the meson pairs are not eigenstates of the heavy quark spin. The decomposition of \(P\)-wave states of meson pairs in terms of the heavy-quark-pair spin states is considered in the channel with \(J^{PC}=1^{--}\), which is directly produced in \(e^+e^-\) annihilation. Specific processes are suggested for experimental study of the effects of the mixing with heavy meson pairs and of the internal spin structure of bottomonium and charmonium resonances.