  We demonstrate that spectrally diverse multiple magnetic dipole resonances
can be excited in all-dielectric structures lacking rotational symmetry, in
contrast to conventionally used spheres, disks or spheroids. Such multiple
magnetic resonances arise from hybrid Mie-Fabry-P\'{e}rot modes, and can
constructively interfere with induced electric dipole moments, thereby leading
to novel multi-frequency unidirectional scattering. Here we focus on elongated
dielectric nanobars, whose magnetic resonances can be spectrally tuned by their
aspect ratios. Based on our theoretical results, we suggest all-dielectric
multimode metasurfaces and verify them in proof-of-principle microwave
experiments. We also believe that the demonstrated property of multimode
directionality is largely responsible for the best efficiency of all-dielectric
metasurfaces that were recently shown to operate across multiple telecom bands.
