A study of the interaction of light with a certain kind of nanoparticle –a core–shell nanoparticle with the shell being of the multilayer hyperbolic metamaterial (HMM) kind– was reported before (Baqir et al. (2021)). However, the study had certain limitations regarding the choice of filling fraction used in the construction of the HMM shell. Herein, the constraints were highlighted and an attempt was made to obtain an appropriate formula for the effective dielectric function of the system.