MAB phases are layered materials combining metallic and ceramic attributes. Their ternary compositions, however, have been limited to a few elemental combinations which makes controlled and tailored properties challenging. Inspired by the recent discovery of Mo4/3Y2/3AlB2 and Mo4/3Sc2/3AlB2i-MAB phases, i.e., quaternary layered MAB phases with in-plane chemical order, we perform an extensive first-principles study to explore formation of chemical order and solid-solutions upon metal alloying of M2AB2 phases of 1092 compositions (M from group 3 to 9 and A = Al, Ga, In, Si, Ge, Sn). This large dataset provides 39 chemically ordered (i-MAB) and 52 solid solution (MAB) phases that are predicted to be thermodynamically stable at typical synthesis temperatures, of which a majority have not yet been experimentally reported. The possibility for realizing both i-MAB and solid solution MAB phases, combined with the multiple elemental combinations previously not observed in these boride-based materials, allows for an increased potential for property tuning and potential chemical exfoliation into 2D derivatives.