Beyond S\'ersic + exponential disc morphologies in the Coma Cluster
  [abridged] We explore the diversity of internal galaxy structures in the Coma
cluster across a wide range of luminosities ($-17$\,$>$\,$M_g$\,$>$\,$-22$) and
cluster-centric radii ($0$\,$<$\,$r_{\rm{cluster}}$\,$<$\,1.3 $r_{200}$)
through analysis of deep Canada-France-Hawaii Telescope $i$ band imaging. We
present 2D multi-component decomposition via GALFIT, encompassing a wide range
of candidate model morphologies with up to three photometric components.
Particular focus is placed on early-type galaxies with outer discs (i.e. S0s),
and deviations from simple (`unbroken') exponential discs. Rigorous filtering
ensures that each model component provides a statistically significant
improvement to the goodness-of-fit. The majority of Coma cluster members in our
sample (478 of 631) are reliably fitted by symmetric structural models. Of
these, 134 ($28\%$) are single S\'{e}rsic objects, 143 ($30\%$) are
well-described by 2 component structures, while 201 ($42\%$) require more
complex models. Multi-component S\'{e}rsic galaxies resemble compact
psuedobulges ($n\sim$\,2, $R_e \sim$\, 4 kpc) surrounded by extended
Gaussian-like outer structures ($R_e > 10$ kpc). 11\% of galaxies ($N=52$)
feature a break in their outer profiles, indicating `truncated' or
`anti-truncated' discs. Beyond the break radius, truncated galaxies are
structurally consistent with exponential discs, disfavouring physical
truncation as their formation mechanism. Bulge luminosity in anti-truncated
galaxies correlates strongly with galaxy luminosity, indicating a
bulge-enhancing origin for these systems. Both types of broken disc are found
overwhelmingly ($>70\%$) in `barred' galaxies, despite a low measured bar
fraction for Coma ($20\pm2\%$). Thus, galaxy bars play an important role in
formation of broken disc structures. No strong variation in galaxy structure is
detected with projected cluster-centric radius.
