The observation by BESIII and LHCb of states with hidden charm and open strangeness ($cbar c qbar s$) presents new opportunities for the development of a global model of heavy-quark exotics. Here we extend the dynamical diquark model to encompass such states, using the same values of Hamiltonian parameters previously obtained from the nonstrange and hidden-strange sectors. The large mass splitting between $Z_{cs}(4000)$ and $Z_{cs}(4220)$ suggests substantial SU(3)$_{rm flavor}$ mixing between all $J^P ! = ! 1^+$ states, while their average mass compared to that of other sectors offers a direct probe of flavor octet-singlet mixing among exotics. We also explore the inclusion of $eta$-like exchanges within the states, and find their effects to be quite limited. In addition, using the same diquark-mass parameters, we find $P_c(4312)$ and $P_{cs}(4459)$ to fit well as corresponding nonstrange and open-strange pentaquarks.
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