  The near-absence of compact massive quiescent galaxies in the local Universe
implies a size evolution since $z\sim2.5$. It is often theorised that such `red
nuggets' have evolved into today's elliptical (E) galaxies via an E-to-E
transformation. We examine an alternative scenario in which a red nugget
develops a rotational disc through mergers and accretion, say, at $1\lesssim
z\lesssim2$, thereby cloaking the nugget as the extant bulge/spheroid component
of a larger, now old, galaxy. We have performed detailed, physically-motivated,
multi-component decompositions of a volume-limited sample of 103 massive
($M_*/\rm M_{\odot} \gtrsim 1\times 10^{11}$) galaxies within 110\,Mpc. Among
our 28 galaxies with existing elliptical classifications, we found that 18 have
large-scale discs, and two have intermediate-scale discs, and are reclassified
here as lenticulars (S0) and elliculars (ES). The local spheroid stellar mass
function, size-mass diagram and bulge-to-total ($B/T$) flux ratio are
presented. We report lower-limits for the volume number density of compact
massive spheroids, $n_\mathrm{c,Sph}\sim (0.17$-$1.2) \times 10^{-4}\,\rm
Mpc^{-3}$, based on different definitions of `red nuggets' in the literature.
Similar number densities of local compact massive bulges were reported by de la
Rosa et al. using automated two-component decompositions and their existence is
now abundantly clear with our multi-component decompositions. We find
disc-cloaking to be a salient alternative for galaxy evolution. In particular,
instead of an E-to-E process, disc growth is the dominant evolutionary pathway
for at least low-mass ($1\times10^{10}<M_*/\rm M_{\odot} \lessapprox 4 \times
10^{10}$) red nuggets, while our current lower-limits are within an alluring
factor of a few of the peak abundance of high-mass red nuggets at $1\lesssim
z\lesssim2$.
