  One observational prediction for Type Ia supernova (SNe Ia) explosions
produced through white dwarf-white dwarf collisions is the presence of bimodal
velocity distributions for the $^{56}$Ni decay products, although this
signature can also be produced by an off-center ignition in a delayed
detonation explosion. These bimodal velocity distributions can manifest as
double-peaked or flat-topped spectral features in late-time spectroscopic
observations for favorable viewing angles. We present nebular-phase
spectroscopic observations of 17 SNe Ia obtained with the Large Binocular
Telescope (LBT). Combining these observations with an extensive search of
publicly available archival data, we collect a total sample of 48 SNe Ia and
classify them based on whether they show compelling evidence for bimodal
velocity profiles in three features associated with $^{56}$Ni decay products:
the [Fe II] and [Fe III] feature at $\sim5300$ \r{A}, the [Co III]
$\lambda5891$ feature, and the [Co III] and [Fe II] feature at $\sim6600$
\r{A}. We identify 9 bimodal SNe in our sample, and we find that these SNe have
average peak $M_V$ about 0.3 mag fainter than those which do not. This is
consistent with theoretical predictions for explosions created by nearly
head-on collisions of white dwarfs due to viewing angle effects and $^{56}$Ni
yields.
