  We study the regularity and large-time behavior of a crowd of species driven
by chemo-tactic interactions. What distinguishes the different species is the
way they interact with the rest of the crowd: the collective motion is driven
by different chemical reactions which end up in a coupled system of parabolic
Patlak-Keller-Segel equations. We show that the densities of the different
species diffuse to zero provided the chemical interactions between the
different species satisfy certain sub-critical condition; the latter is
intimately related to a log-Hardy-Littlewood-Sobolev inequality for systems due
to Shafrir & Wolansky. Thus for example, when two species interact, one of
which has mass less than $4\pi$, then the 2-system stays smooth for all time
independent of the total mass of the system, in sharp contrast with the
well-known breakdown of one specie with initial mass$> 8\pi$.
