I have thought of a society which got disappointed by the other government forms and decided to engineer the Emperor. They selected the best genes of their race and they cloned an Emperor to rule them all.
Genetically engineering an emperor isn't something that can be done by "society" as a whole. There must be a powerful organization that has the technological refinement and source material to produce a candidate (e.g the Tleilaxu in Dune) and a position of power or supremacy to impose him/her/it as the legitimate emperor; different factions would be expected to support their own emperors, even if they all agree on the basic premise of building a good ruler, and there might be severe civil wars.
When the emperor dies or retires, the problem returns. Is the emperor-making group permanently at the helm, avoiding disruptions with an easily installed new emperor? Or every succession causes a renewed conflict between factions (example: USA presidential elections)? Or it never happened yet because the first emperor is still ruling (example: humanity in Warhammer 40000)?
You could have mortal but very long-lived emperors that stress the self-preservation of the emperor-building system to the breaking point: where are, after a few centuries, the cloning facilities, the genetic engineers, the political support (in elections or other procedures that have not taken place for generations), etc.? The game could be about the emperor successfully organizing his succession and retirement in hard times.
The Pern novels by Anne McCaffrey are an excellent example of this subject; a planet struggles to maintain astronomy, various races of domesticated dragons, an idle paramilitary corps of telepathic dragonriders, and other expensive things that are only useful against alien critters who fall from the sky at intervals of several generations and are just about as terrible as an empire without his head, with coverage of how it went the first time (heroic emergency mode), how traditions and institutions were established, abandoned, revived and applied, and how great people made the difference.
In general, this system of making emperors is compatible with different government systems, possibly at the same time; true democracy if different candidates are offered for election and produced disinterestedly as a matter of duty and prestige, aristocracy if candidates are derived from the gene pool of certain families, rather corrupt oligarchy if candidates are expected, or engineered, to further the interests of their makers; if the emperor controls succession it would be a true autocratic monarchy; if there isn't much of an election it would be some kind of oligarchy or technocracy.
A custom made emperor candidate would, in most cases, avoid the internal struggles within factions that are usually implied in a normal election: no place for ambitious people who want to be emperor, no need to kill off everyone above yourself in a succession line, etc.