Consortium imperii

Consortium imperii is a Latin term dating from the Roman Dominate, denoting the sharing of imperial authority between two or more emperors, each hence designated as "consors imperii", i.e. "partner in (exercising) "imperium"", either as formal equals or in subordination, in which case the junior was often the senior's designated heir—not necessarily the natural one—and successor. In theory, this arrangement served to share the burden of government and ensure smooth succession, as rivalry at these moments was a major threat to the stability of the Empire; however, in practice the net result was often more civil war.
Although in political reality "adoption" was an alternative technique to aim for the same result in terms of succession (and which succeeded in producing one genealogically "false" but politically satisfactory dynasty of so-called "Adoptive Emperors"), constitutionally, this was a horror as the republic had never been abandoned in law. Thus monarchical succession in the Principate, however realistic, was officially out of the question, and this stigma persisted in the Dominate, despite the obviously monarchical trappings adopted by the emperors in this era. 'Designation', rather than simple adoption, could at least be justified by qualitative criteria.