Second-order topological insulators (SOTIs) have recently attracted much attention due to their capability to support lower-dimensional topological states, namely, the corner states. Here, we demonstrate that properly designed supercell metasurfaces can support photonic corner states, meanwhile further serving as an ideal platform for the implementations of topological polaritons and dynamically reconfigurable corner states by assembling two-dimensional materials. Such metasurfaces consist of an array of finite-sized SOTIs mimicking the two-dimensional Su–Schrieffer–Heeger model. We reveal that the topological transition happens in unit cells without the bandgap, and nondegenerate multipolar corner states emerge in the supercell metasurface due to the inter- and intrasupercell coupling effects. Especially since these corner states are above the light line of the metasurface, we realize the collective stimulation of the two dipolar corner states and their superposition state via far-field excitation. By stacking monolayer hexagonal boron nitride film onto the metasurface, we further achieve the topological phonon polaritons through the strong coupling between the corner state and the phonon, which is confirmed by the Rabi splitting as well as anticrossing behavior emerging in the transmission spectra. Furthermore, we reveal the robustness of the corner state and strong coupling by introducing defects into the metasurface. Finally, tunable corner state and strong coupling with on-demand control are realized by assembling monolayer graphene onto the metasurface. Our theoretical study proposes a unique hybrid-material platform for topological polaritonics and reconfigurable topological photonics, which can promote large-area topological applications in practice.