The polarization response of molecules ormeta-atoms to external electric and magnetic fields, which defines the electromagnetic properties of materials, can either be direct (electric field induces electric moment and magnetic field induces magnetic moment) or indirect (magnetoelectric coupling in bianisotropic scatterers). Earlier studies suggest that there is a fundamental bound on the indirect response of all passive scatterers: It is believed to be always weaker than the direct one. In this paper, we prove that there exist scatterers which overcome this bound substantially. Moreover, we show that the amplitudes of electric and magnetic polarizabilities can be negligibly small as compared to the magnetoelectric coupling coefficients. However, we prove that if at least one of the direct-excitation coefficients vanishes, magnetoelectric coupling effects in passive scatterers cannot exist. Our findings open a way to a new class of electromagnetic scatterers and composite materials.