The interplay between localized surface plasmon (LSP) resonances and their collective responses, known as surface lattice resonances (SLRs), in metal nanoparticle arrays can lead to resonances with high Q-factors (∼100). These responses have in the past usually been studied for LSP resonances in the plane of the array of the nanoparticles (assumed to be nonmagnetic), thus restricting efficient coupling to particles separated along a specific direction. In the present study, we demonstrate that LSPs oscillating perpendicular to the plane of the surface can lead to stronger inter-particle coupling, which enhances the SLRs. This stronger coupling occurs because the out-of-plane oscillations can couple in all directions within the plane of the array. We study the resulting SLRs for square and hexagonal lattices using the discrete-dipole approximation, and we predict much larger Q-factors in the wavelength range near 650 nm. This prediction suggests that SLRs could be very useful in enhancing various optical processes, and in many applications such as sensing and nonlinear optical wave mixing.