  The observation by BESIII and LHCb of states with hidden charm and open
strangeness ($c\bar c q\bar s$) 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.
