  The atmospheric depth where the energy deposit profile of secondary particles
from extensive air showers (EAS) reaches its maximum, $X_{\rm max}$, is related
to the primary particle mass. The mass composition of the ultra-high energy
cosmic rays (UHECRs) can be inferred from measurements of $X_{\rm max}$
distributions in each energy interval, by fitting these distributions with
Monte Carlo (MC) templates for four primary species (p, He, N and Fe). On the
basis of simulations, we show that a high abundance of some intermediate
elements in the $X_{\rm max}$ distributions, e.g. Ne or Si, may affect the
quality of the fit and also the reconstructed fractions of different species
with respect to their true values. We propose a method for finding the "best
combination" of elements in each energy interval from a larger set of primaries
(p, He, C, N, O, Ne, Si and Fe) which best describes the $X_{\rm max}$
distributions. Applying this method to the $X_{\rm max}$ distributions measured
by the Pierre Auger Observatory (2014), we found that the "best combination" of
elements which best describe the data suggest the presence of Ne or Si in some
low energy bins for the EPOS-LHC model.
