  We construct spectra of supernovae interacting strongly with a circumstellar
medium (CSM) by adding SN templates, a black-body continuum and an
emission-line spectrum. In a Monte Carlo simulation we generate more than 800
spectra, distribute them to 10 different classifiers and study how the
different simulation parameters affect the appearance of the spectra. SNe IIn
showing some structure over the continuum were characterized as SNe IInS. We
demonstrate that the flux ratio of the underlying SN to the continuum fv is the
most important parameter determining the spectral classification. Thermonuclear
SNe get progressively classified as Ia-CSM, IInS and IIn as fv decreases. The
transition between Ia-CSM and IInS occurs at fv~0.2-0.3. It shown that SNe
Ia-CSM are found at the magnitude range -19.5> M >-21.6, in good agreement with
observations, and that the faintest SN IIn that can hide a SN Ia has M = -20.1.
The sample of SNe Ia-CSM shows an association with 91T-like SNe Ia. Our
experiment does not support that this association is due to a luminosity bias
(91T-like being brighter than normal Ia). We therefore conclude that this
association has real physical origins and we propose that 91T-like explosions
result from single degenerate progenitors. Despite the similarities between SNe
Ibc and SNe Ia, the number of misclassifications between these types was small
and mostly at low S/N. Combined with the luminosity function needed to
reproduce the observed SN Ia-CSM luminosities, it is unlikely that SNe Ibc
constitute an important contaminant within this sample. We show how Type II
spectra transition to IIn and how the Ha profiles vary with fv. SNe IIn fainter
than M = -17.2 are unable to mask SNe IIP brighter than M = -15. A simulation
including radiative transfer shows that our simplified model is a good first
order approximation. The spectra obtained are in good agreement with real data.
