Total maximum luminosity of a SN interacting with a CSM (i.e. together with the continuum contribution), as a function of the underlying SN maximum luminosity and the ratio f_V. The graph focuses on the magnitude region occupied by SNe Ia (vertical dashed lines). As shown before (e.g. Fig. 5), the spectrum of the SN interacting strongly with the CSM will receive different classifications, depending on the value of f_V (diagonal dashed lines). SNe in the red-coloured area will be classified as a IIn (including IInS in this project) and SNe in the dark-grey area as Ia-CSM. Objects in the cyan area can be classified with their exact sub-type (e.g. 91T-like), while the light-grey areas represent transitional zones where more classifications are possible. It is therefore possible to determine the (un-extincted) magnitude region for SNe Ia-CSM (−19.5 >M_V> −21.6) and the lower luminosity limit for a SN IIn that can hide a SN Ia (M_V< −20.1). These regions are illustrated by the red and grey vertical bars on the top left.