MAB phases (MABs) are atomically-thin laminates of ceramic/metallic-like layers, having made a breakthrough in the development of 2D materials. Though offering a vast chemical and phase space, relatively few MABs have been synthesised. To guide experiments, we perform high-throughput ab initio screening of MABs that combine group 4-7 transition metals (M); Al, Si, Ga, Ge, or In (A); and boron (B) focusing on their phase stability trends and mechanical properties. Considering the 1:1:1, 2:1:1, 2:1:2, 3:1:2, 3:1:3, and 3:1:4 M:A:B ratios and 10 phase prototypes, synthesisability of a single-phase compound for each elemental combination is estimated through formation energy spectra of competing dynamically stable MABs. Based on the volumetric proximity of energetically-close phases, we identify systems in which volume-changing deformations may facilitate transformation toughening. Subsequently, chemistry- and phase-structure-related trends in the elastic stiffness and ductility are predicted using elastic-constants-based descriptors. The analysis of directional Cauchy pressures and Young's moduli allows comparing mechanical response parallel and normal to M-B/A layers. The suggested promising MABs include Nb 3 AlB 4 , Cr 2 SiB 2 , Mn 2 SiB 2 or the already synthesised MoAlB.