Metasurfaces have recently gained extensive interest because of their extraordinary optical behavior as artificial material interfaces with ultrahigh compactness. In this framework, dielectric platforms have newly become very promising for nonlinear nanophotonics, providing opportunities, especially for ultrafast optical switching, and high harmonic generation, opening the research field of nonlinear metaoptics. Up to now, nonlinear metaoptics have been mostly explored using single metasurfaces. However, in a long-term vision, the stacking of optical metasurfaces, very challenging in terms of fabrication, is one key goal of this research field. Here, we demonstrate a three-layer metasurface in the AlGaAs-on-insulator platform, which improves the second harmonic generation efficiency by more than one order of magnitude with respect to its one-layer counterpart. Our achievement paves the way toward phase-shaping multilayer and multifunctional all-dielectric metasurfaces.