  We report the detection of a strong HI 21-cm absorption system at z=0.5344,
as well as a candidate system at z=0.3389, in the sight-line towards the z=2.64
quasar MG J0414+0534. This, in addition to the absorption at the host redshift
and the other two intervening absorbers, takes the total to four (possibly
five). The previous maximum number of 21-cm absorbers detected along a single
sight-line is two and so we suspect that this number of gas-rich absorbers is
in some way related to the very red colour of the background source. Despite
this, no molecular gas (through OH absorption) has yet been detected at any of
the 21-cm redshifts, although, from the population of 21-cm absorbers as a
whole, there is evidence for a weak correlation between the atomic line
strength and the optical--near-infrared colour. In either case, the fact that
so many gas-rich galaxies (likely to be damped Lyman-alpha absorption systems)
have been found along a single sight-line towards a highly obscured source may
have far reaching implications for the population of faint galaxies not
detected in optical surveys, a possibility which could be addressed through
future wide-field absorption line surveys with the Square Kilometre Array.
