Nonlinear-optical effects in magnetic composite nanostructures are of fundamental and practical interest. Here we study, on the micro- and macro-scales, the nonlinear-optical and magnetooptical response of metasurfaces made of arrays of magnetic Co/Au plasmonic particles on the crystalline garnet layer. We find a manyfold enhancement of the efficiency of the optical second harmonic generation as well as a strong modification of the magnetooptical response of this metasurface as compared to the pure garnet film. Numerical modelling of the local electromagnetic field confirms these findings.