  We present a revised version of our automated technique using Gaussian
processes (GPs) to detect Damped Lyman-$\alpha$ absorbers (DLAs) along quasar
(QSO) sightlines. The main improvement is to allow our Gaussian process
pipeline to detect multiple DLAs along a single sightline. Our DLA detections
are regularised by an improved model for the absorption from the Lyman-$\alpha$
forest which improves performance at high redshift. We also introduce a model
for unresolved sub-DLAs which reduces mis-classifications of absorbers without
detectable damping wings. We compare our results to those of two different
large-scale DLA catalogues and provide a catalogue of the processed results of
our Gaussian process pipeline using 158 825 Lyman-$\alpha$ spectra from SDSS
data release 12. We present updated estimates for the statistical properties of
DLAs, including the column density distribution function (CDDF), line density
($dN/dX$), and neutral hydrogen density ($\Omega_{\textrm{DLA}}$).
