Intense researches on new kinds of materials, especially those with marked multi-principal-element character, currently give rise to all-intricate multiphase environments, for which reliably predicting structure and stability becomes extremely difficult to achieve with macroscopic phenomenological modellings.The purpose of this work is to demonstrate how this issue can be overcome by sticking down to the atomic scale, through ab initio-based thermodynamics within the Independent-Point-Defect Approximation (IPDA), which offers an efficient framework to investigate systems involving various chemistries and crystallographies.As a case study of significant intricacy, we consider ternary Al-B-Ti viewed as an approximant for Al-based alloys reinforced with TiB2 particles and including AlB2 and Al3Ti additional compounds.Firstly, our IPDA investigations reveal unexpected discrepancies among neighbouring metallic borides, and predict point defect structures at odds with earlier pictures commonly employed hitherto, which suggests that many complex compounds may suffer from inadequate phenomenological modellings.Furthermore, we show that far-reaching conclusions on phase stability can be drawn only if the scope of analysis is broadened up to encompass global multiphase IPDA-based thermodynamics, a task which constitutes the core and the methodological originality of this work.Our approach thus provides reliable arguments to interpret the occurrence of various kinds of poorly known compounds, as illustrated by the controversial behaviour of Al3Ti and AlB2 in TiB2-reinforced Al-based composites.Finally, our work allows to conclude that the robust and handsome IPDA approach can be extended to highly intricate multiphase situations, e.g. to investigate other classes of multiphase multi-principal-element materials, which due to the presence of complex crystal structures can hardly be explored by alternative methods.