We design and numerically investigate an all-dielectric metamaterial, consisting of silicon ring and disk with a missing wedge-shaped slice lying on a silica substrate that realizes multiple switching based on toroidal and trapped dipole magnetic responses. Such two responses can be dynamically switched on and off simultaneously only through changing polarization of incident light, and the direction of toroidal dipole can be rotated 90 deg in two separate frequency regimes. Further, the maximum values of amplitude modulation depth around magnetic responses almost reach 100%, respectively. Multiple switching based on such magnetic responses shows potential applications in active filters, sensors, and switching.