To shed a new light on the complex microstructural evolution in the Ti-Al-Mo system, we employ ab initio calculations to study bcc-fcc structural transformations of ordered βo-TiAl(+Mo) and disordered β-TiAl(+Mo) to ordered γ-TiAl(+Mo) and hypothetically assumed disordered γdis-TiAl(+Mo) alloys, respectively. In particular, tetragonal (Bain's path) and trigonal transformations are combined with the concept of special quasirandom structures (SQS) and examined. Our calculations of the ordered phases show that the βo→γ tetragonal transformation of TiAl is barrierless, i.e., proceeds spontaneously, reflecting the genuine structural instability of the βo phase. Upon alloying of ≈7.4at.% Mo, a small barrier between βo and γ-related local energy minima is formed. Yet a higher Mo content of ≈9at.% leads to an opposite-direction barrierless transformation γ→βo, i.e., fully stabilizing the βo phase. Considering the disordered phases, the β-Ti0.5Al0.5-xMox and γdis-Ti0.5Al0.5-xMox are energetically very close. Importantly, for all here-considered compositions up to 11at.% of Mo, a small energy barrier separates β-TiAl(+Mo) and γdis-TiAl(+Mo) energy minima. Finally, a trigonal path was studied as an alternative transformation connecting disordered β and γdis-TiAl phases, but it turns out that it exhibits an energy barrier over 60meV/at. which, in comparison to the Bain's path with 9meV/at. barrier, effectively disqualifies the trigonal transformation for the TiAl system.