This comparison allows for a few insights into the nature of the additional peak in the classical model. First, in contradiction to previous discussions in the literature, the plots illustrate that the third peak does not require a negative real part of the permittivity. In all examples it is clearly larger than zero, yet if the imaginary part becomes too large, the peak becomes visible. In fact, Real(ϵ) is not responsible for the additional peak to arise but it is the large imaginary part of the shell permittivity, that causes a maximum in the imaginary part of the particle polarizability α. In contrast to the two polariton resonances, the additional peak in the classical model in not caused by a minimum in the denominator of α, but by a maximum in its numerator caused by the large Im(ϵ class ) (see also Supplementary Information). To suppress the peak, it is therefore necessary to decrease its maximum (without suppressing Real(ϵ) too much). This is exactly the effect of the power broadening. In fact, one could argue that the additional peak does not represent a single new mode, at all. An (eigen-)mode of a spherical particle is characterized by a vanishing denominator of the corresponding scattering coefficients and consequently of the polarizability α. This is not the case for the additional peak in our parameter set of the classical model. Having said that, the classical model does not contradict standard models for strong coupling in predicting a novel or polariton state . We show that the third peak only emerges due to a highly polarizable and absorptive shell medium.