How would an immortal emperor maintain continuity with a mortal government?

*This is specifically for an empire where hereditary rule is expected (e.g. Rome), and the immortal ruler has been emperor for a long time.*<br><br>Assuming the emperor is fairly benevolent, how would they maintain a sense of continuity of rule, assuming they have to periodically change their identity to remain in power?<br><br>Would it even be possible to maintain such a ruse over a long period of time?<br><br>What about an immortal advisor? All I can think of is the Chinese Mandate of Heaven.