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.plasmon-exciton polaritons (plexcitons [60]) may become a modern platform for ultrafast active control of light [38,39,61] and room temperature polariton lasing [62].Over the past few years, the 2D materials research has grown into the broader field, which includes the study of van der Waals heterostructures [63] and transdimensional materials [64]. Similar to van der Waals materials, which for some applications are more effective in a fewlayer configuration than in a monolayer one [58,59,65], the applicability of metasurfaces can be dramatically improved by going to the few layers. The multiplication of metasurface layers, while retaining a relatively low level of losses and fabrication simplicity, can provide higher efficiency and more degrees of freedom for manipulating the phase, amplitude, polarization, propagation, and dispersion of light [66,67]. Moreover, the layers interaction results in additional effects, including near-field coupling, WG modes, and multiple wave interference [68]. The WG effects enable us to control polarization and phase of the transmitted light simultaneously [69], while multiple interference effects can be used to cancel the undesired light and enhance the efficiency of antireflection coatings [70], polarization converters [71,72], and metalenses [73]. Near-field coupling generates a magnetic resonance inside the structure, which being effectively coupled to an in-layer electric resonance allows us to realize perfect absorbers and reflectors [74--76]. Such a magnetic ...