In the quest for finding novel thermodynamically stable, layered, MAB phases promising for synthesis, we herein explore the phase stability of ternary MAB phases by considering both orthorhombic and hexagonal crystal symmetries for various compositions (MAB, M2AB2, M3AB4, M4AB4, and M4AB6 where M = Sc, Y, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W, Mn, Fe, and Co, A = Al, Ga, and In, and B is boron). The thermodynamic stability of seven previously synthesized MAB phases is confirmed, three additional phases are predicted to be stable, and 23 phases are found to be close to stable. Furthermore, the crystal symmetry preference for forming orthorhombic or hexagonal crystal structures is investigated where the considered Al-based MAB phases tend to favour orthorhombic structures whereas Ga- and In-based phases in general prefer hexagonal structures. The theoretically predicted stable MAB phases along with the structural preference is intended to both guide experimental efforts and to give an insight into the stability for different crystal symmetries of MAB phases.