The BESIII Collaboration has observed a candidate for a $c\overline{c}s\overline{u}$ tetraquark $Z_{cs}$ at $(3982.5_{-2.6}^{+1.8}±2.1)$ $MeV$ and width $(12.8_{-4.4}^{+5.3}±3.0)$ $MeV$, while the LHCb Collaboration has observed a $Z_{cs}$ candidate in the $J/\Psi K^-$ channel with mass of $(4003±6_{-14}^{+4})$ and width $(131±15±26)$ $MeV$. In this paper, we examine the possibility that these two states are distinct eigenstates of a mixing process similar to that which gives rise to two axial-vector mesons labeled by the Particle Data Group [P. Zyla et al., Prog. Theor. Exp. Phys. 6, 083C01 (2020)] $K_1 (1270)$ and $K_1 (1400)$. The main point is that on top of a $c\overline{c}$ pair of the $Z_{cs}$ states have the same light quark content as the $K_1-s$. In the compact tetraquark picture, this implies several additional states, analogous to members of the $K_1$ nonet. These states have not yet been observed; nor are they required in the molecular approach. Thus, experimental discovery or exclusion of these extra states will be a critical test for competing models of exotic mesons with hidden charm.