Great progress has been achieved in fabricating arbitrary metal nanoparticle shapes and geometries in order to control their linear optical properties. However, their nonlinear optical properties, particularly their second-order response, are frequently overlooked. Exploiting the nonlinear responses of metal nanoparticles opens another exciting avenue for developing nanoscale photonics applications. Second-harmonic generation (SHG) from metal nanoparticles is typically attributed to electric dipole excitations at their surfaces, but nonlinearities involving higher multipole effects, such as magnetic dipole interactions, electric quadrupoles, etc., may also be significant due to strong nanoscale gradients in the local material properties and fields. The nanoscale nonlinear optical processes in metal nanoparticles are not well-understood at present, and determining the sources of the SHG response can be arduous. In order to study the role of higher multipoles in the second-order response of gold nanoparticle arrays, we propose SHG measurements employed in both transmission and reflection geometries. Due to different radiative properties of the various multipoles in the forward and backward directions, the presence of multipoles should lead to opposing interference effects in the two directions. Strong polarization dependence of the response can modify the relative strengths of the interfering terms, thereby allowing electric-dipole and higher-multipole contributions to the overall SHG response to be distinguished. Analysis of the measured polarization dependencies would thus provide further knowledge of the mechanisms underlying the nanoscale SHG process in gold nanoparticles.