For thick TEM samples, an incident electron can excite several plasmons and multiple peaks can occur, for instance, two or more plasmons can be excited by a single primary electron, inducing double and/or triple plasmon peaks in the EELS spectrum.
A thin specimen can avoid multiple scattering which obscures the core-loss edges. That is, the sample should be so thin that the plasmon peak is smaller than one-tenth of the zero loss.
The 3rd plasmon peak normally is not significant unless the
thickness is approximately equal to the plasmon mean free path of the analyzing materials.