A general strategy for the realization of electric and magnetic quasi-trapped modes located at the same spectral position is presented. This strategy's application makes it possible to design metasurfaces allowing switching between the electric and magnetic quasi-trapped modes by changing the polarization of the incident light wave. The developed strategy is based on two stages: the application of the dipole approximation for determining the conditions required for the implementation of trapped modes at certain spectral positions and the creation of the energy channels for their excitation by introducing a weak bianisotropy in nanoparticles. Since excitation of trapped modes results in a concentration of electric and magnetic energies in the metasurface plane, the polarization switching provides possibilities to change and control the localization and distribution of optical energy at the sub-wavelength scale. A practical method for spectral tuning of quasi-trapped modes in metasurfaces composed of nanoparticles with a preselected shape is demonstrated. As an example, the optical properties of a metasurface composed of silicon triangular prisms are analyzed and discussed.