We design and numerically investigate an all-dielectric metasurface, constructed of four open resonant rings described by the group C_s and located with a cross-shaped resonator between them, that realizes double toroidal switching, in which switching from a toroidal dipole to a quadrupole response occurs in two separate frequency regimes. It is shown that the toroidal dipole can be dynamically switched on, whereas the pronounced toroidal quadrupole can be switched off simultaneously at orthogonal orientations from same metasurface, and vice versa, through changing the polarization of the incident light. The maximum value of modulation depth for the toroidal dipole and quadrupole responses reached 76% and 83%, respectively. Active switching of a toroidal dipole into a quadrupole has potential applications in designing efficient filters and modulators.