We complement our study on the doping and disorder in Co ₂ MnZ compounds [I. Galanakis, K. Özdoğan, B. Aktaş, and E. Şaşıoğlu, Appl. Phys. Lett. 89, 042502 (2006) and K. Özdoğan, E. Şaşıoğlu, B. Aktaş, and I. Galanakis, Phys. Rev. B 74, 172412 (2006)] to cover also the quaternary Co ₂[Y_1-xY_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, and 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 density of states 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 considerably lowers the majority density of states at the Fermi level and when combined with an element belonging to the Si column, it can even destroy half-metallicity.