An artificial magnetic response is not only intellectually intriguing but also key to multiple applications. While previously suitably structured metallic particles and high-permittivity dielectric particles have been used for this purpose, here, we highlight the possibility of exploiting lattice effects to significantly enhance an intrinsically weak magnetic dipole moment of a periodically arranged scatterer. We identify the effective magnetic dipole moment as it is modulated by the lattice

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... coupled to other electromagnetic multipole moments the scatterer can sustain. Besides a more abstract consideration on the base of parametrized Mie coefficients to study the theoretical upper limit, we present an actual particle that shows an enhancement of the magnetic dipole moment by 100 with respect to what is attainable as a maximal value for an isolated particle.