We report the results of density functional theory for 39 clusters AxBy (x + y = 10 or 12) where A and B are metals from group 1, 2, 11, 12, 13, or 14 of the periodic table. The chemical compositions were chosen to satisfy an electronic shell closing criterion. We performed an unbiased search for the global minimum (GM) by taboo search in descriptor space in each case. Eight of the 39 putative GM are cages even though none of the clusters contains gold, a metal with a well known propensity to form cages. These cages are large enough to accommodate a dopant atom with an atomic radius varying between 0.7 Å and 1.2 Å. The chemical compositions most likely to produce cages have an element of group 11 alloyed with an element of group 2, 12, or 13.