  We complement our study on the doping and disorder in Co$_2$MnZ compounds [I.
Galanakis \textit{et al.}, Appl. Phys. Lett. \textbf{89}, 042502 (2006) and K.
\"Ozdo\~gan \textit{et al.}, Phys. Rev. B \textbf{74}, (2006)] to cover also
the quaterarny Co$_2$[Y$_{1-x}$Y$^*_x$]Z compounds with the lower-valent
transition metals Y,Y$^*$ being Cr, Mn or Fe and the sp atom Z being one of Al,
Ga, Si, Ge, Sn. This study gives a global overview of the magnetic and
electronic properties of these compounds since we vary both Y and Z elements.
Our results suggest that for realistic applications the most appropriate
compounds are the ones belonging to the families Co$_2$[Mn$_{1-x}$Cr$_x$]Z with
$x>0.5$ irrespectively of the nature of the $sp$ atoms since they combine high
values of majority DOS at the Fermi level due to the presence of Cr, and
half-metallicity with large band-gaps. On the other hand the presence of Fe
lowers considerably the majority density of states at the Fermi level and when
combined with an element belonging to the Si-column, it even can destroy
half-metallicity.
