The nebular-epoch spectrum of the rapidly declining, "transitional" type Ia supernova (SN) 2007on showed double emission peaks, which have been interpreted as indicating that the SN was the result of the direct collision of two white dwarfs. The spectrum can be reproduced using two distinct emission components, one red-shifted and one blue-shifted. These components are similar in mass but have slightly different degrees of ionization. They recede from one another at a line-of-sight speed larger than the sum of the combined expansion velocities of their emitting cores, thereby acting as two independent nebulae. While this configuration appears to be consistent with the scenario of two white dwarfs colliding, it may also indicate an off-centre delayed detonation explosion of a near Chandrasekhar-mass white dwarf. In either case, broad emission line widths and a rapidly evolving light curve can be expected for the bolometric luminosity of the SN. This is the case for both SNe 2007on and 2011iv, also a transitional SN Ia which exploded in the same elliptical galaxy, NGC 1404. Although SN 2011iv does not show double-peaked emission line profiles, the width of its emission lines is such that a two-component model yields somewhat better results than a single-component model. Most of the mass ejected is in one component, however, which suggests that SN 2011iv was the result of the off-centre ignition of a Chandrasekhar-mass white dwarf.