Recent experimental findings about new nematogenic molecules have reported thermally driven transitions to biaxial phases, which has revived the interest for macroscopic biaxiality. In particular, the simplified interaction model proposed by Straley for molecules endowed with D(2h) symmetry has met renewed interest. In the scenario obtained for phases a unifying character can be captured. There exists a universal feature in the behaviour of one uniaxial order parameter, rebounding at the biaxial-to-uniaxial transition. This finding has been confirmed by means of a Monte-Carlo simulation. Moreover, the phase sequences and the order of the transitions are poorly influenced by one of the interaction parameters.