'Consortium imperii is a Latin word dating from the Roman dominate, denoting the sharing of imperial authority between two or more emperors, hence designated as consors imperii, i.e. 'partner in (exercezing) imperium - either as equals or in subordination (the junior is then often designated heir and successor).

An early case of one emperor, remaining 'sole sovereign' in charge, but designating one junior and successor, was Marcus Aurelius (reigned 161-180AD) - but his son Commodus, which he justly wanted to pass by, managed to seize the throne. Marcus Aurelius Imperator Caesar Marcus Aurelius Antoninus Augustus (April 26, 121 – March 17, 180) was Roman Emperor from 161 to his death in 180. ... Commodus Marcus Aurelius Commodus Antoninus (originally Lucius Aelius Aurelius Commodus) (August 31, 161–December 31, 192 A.D.) was a Roman Emperor who ruled from 180 to 192 A.D. He is often considered to have been one of the worst Roman Emperors, and his reign brought to a close...

Emperor Diocletian attempted an elaborate system with four emperors (two seniors styled Augustus, each with a junior styled Caesar), called the Tetrarchy. Revolutionary was the notion that each was to be simultaneously in permanent charge of one quarter of the empire, not just sharing in central government. The experiment did not live up to its promise, as succession was not smoothened but contention multiplied, so the quadruple emperorship was abonded - not the quarters, which remained as administrative and military divisions called pretorian prefecture, as did the lower level, called diocese, and the smaller size (and larger number) of provinces. The Tetrarchs, a porphyry sculpture sacked from a Byzantine palace in 1204 CE, Treasury of St. ...