  A comprehensive analysis of hybrid TM-TE polarized surface electromagnetic
waves supported by different few-layer anisotropic metasurfaces is presented. A
generalized 4$\times$4 T-matrix formalism for arbitrary anisotropic 2D layers
is developed, from which the general relations for the surface waves
dispersions and scattering coefficients are deduced. Using this formalism and
the effective conductivity approach, the dispersions and iso-frequency contours
(IFCs) topology of the surface waves in various hybrid uniaxial metasurfaces
are studied. The existence of hyperbolic plasmon-exciton polaritons in
plasmon-exciton hybrids and hyperbolic acoustic waves with strong confinement
in both out-of-plane and in-plane directions in uniaxial plasmonic bilayers are
predicted. In plasmonic uniaxial metasurfaces on metal films, the elliptic and
hyperbolic backward surface waves with negative group velocity are predicted
and additional topological transitions in both elliptic and hyperbolic IFCs of
the hybrid surface waves are revealed. Ultrathin twisted uniaxial plasmonic
bilayers are proposed as systems with the IFCs topological transitions highly
sensitive to the layers twist. The developed formalism may become a useful tool
in the calculation of multifunctional few-layer metasurfaces or van der Waals
heterostructures based on 2D materials with in-plane anisotropy, where the
TM-TE polarization mixing must be considered. The predicted effects may open
new horizons in the development and applications of planar optical
technologies.
