Nonlinear metamaterials show potential for realizing flat nonlinear optical devices but are generally lacking in terms of achievable conversion efficiencies. Recent work has focused on enhancing nonlinear processes by utilizing high quality factor resonances, such as collective responses known as surface lattice resonances (SLRs) taking place in periodic metal nanoparticle arrays. Here, we investigate how the dispersive nature of SLRs affects the nonlinear responses of SLR-supporting metasurfaces. Particularly, we measure second-harmonic generation from aluminum nanoparticle arrays and demonstrate that by tilting the sample along two orthogonal directions, the sample can be made multiply-resonant for several pump and second-harmonic signal wavelength combinations. Characterized metasurfaces are estimated to exhibit a second-order susceptibility value of 0.40 pm/V, demonstrating aluminum as a potential material for nonlinear metasurfaces.