Understanding the underlying constitutional mechanisms for the stability of complex phases and comprehending it is crucial to find new materials with desired mechanical and physical properties. In TiAl-alloys with ternary alloying additions orthorhombic phases can form but the effects of different alloying elements on their stability and other properties are only scarcely known. We present a comprehensive study using density functional theory (DFT) within the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) method to determine energetic, and mechanical stability criteria and evaluate the electronic densities of states (DOS) and band structures to understand bonding behavior. The stability of Ti2AlM, as a bulk O-phase in ternary TiAl-based systems is predicted by investigating VB (V, Nb, and Ta) and VIB (Mo, W) group elements as ternary addition M. The electronic density of states and band structure indicate that the ternary elements addition causes charge redistribution through the formation of a bond, which significantly alters the stability and mechanical properties. All investigated compounds exhibit negative formation energies and the calculated elastic constants reveal that all are mechanically stable. For the different O-phase types investigated Ti2AlMo is the most stable and Ti2AlV the least stable when comparing energies of formation. The obtained elastic moduli and Pugh's ratios support the idea that Ti2AlM (M = V, Nb, Ta, Mo, and W) O-phases have attractive mechanical characteristics and exhibit ductility. Among all the systems investigated, Ti2AlMo, and Ti2AlW provide the highest increase in B, G, and E values. Based on the elastic constants also indicators for the mechanical properties, such as Poisson's ratio (ν), and Pugh ratio G/B, are calculated. According to our calculations, the brittle Ti2AlV is harder than the ductile Ti2AlMo. Based on the results of the present study, the Ti2AlM type O-phase is considered a promising constituent for designing new materials in the ternary Ti–Al-M system.