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Non-perturbative high-harmonic generation has recently been observed in the liquid phase, and the underlying mechanism was shown to be different from that in gases and solids. Liquid-phase high-harmonic generation is currently understood in terms of a recollision mechanism with electron trajectories limited by electron scattering. The cut-off energy and its independence of the driving laser parameters are reproduced by this mechanism. However, when the driving laser intensity is increased, no extension of the cut-off energy is observed, which contrasts with the general expectations from most nonlinear media. Here we observe the appearance of a second plateau in high-harmonic generation from multiple liquids (water, heavy water, propanol and ethanol) and explore its origin. From the combined analysis of experimental, computational and theoretical results, we find that electrons recombining at neighbouring molecular sites instead of the ionization site are responsible and verify this feature through the characteristic dependence of the second-plateau yield on the ellipticity of the driving field. We find that the second plateau is dominated by electrons recombining at the first or second solvation shell, relying on hole delocalization. Theoretical results predict the appearance of yet higher plateaus, indicating a general trend. Our work establishes a previously unexplored physical phenomenon in the highly nonlinear optical response of liquid.