We propose a design and perform a theoretical and experimental study of optical properties of a metasurface composed of hexagonal oligomers of dielectric particles that somewhat resemble characteristics of multiferroics. It can maintain both toroidic and antitoroidic orders in the dynamical response on irradiation by a linearly polarized plane wave. These orders originate from the dark states of toroidal dipole moments. Due to the consciously chosen perturbation in the oligomers, the orders are excited at the same frequency by the wave with orthogonal polarization. The excitation of these orders results in different characteristics of the electric near-field localization. This has significant potential for several applications, which are thoroughly discussed.