  Contrary to a paradigm of metal-enhanced fluorescence, unusually thick
dielectric coatings can be very favorable to achieve extreme values of averaged
fluorescence enhancement factor $\bar F\gtrsim 3000$ for emitters located on
the surface, or in the interior, of the shell of Au@dielectric spherical
core-shell particles under realistic conditions, even for the emitters with
100% intrinsic quantum yield. Thick dielectric coatings facilitate high-quality
transverse electric (TE) multipole ($\ell=7$) resonances which are shown as the
major cause for the reported extraordinary values of $\bar F$.
