In modern Tyr, oligarchy refers to a proposed unicameral government system that would put the power in the hands of a Senate populated by literate nobles, with no king (or perhaps a powerless figurehead king).
In the last months of Kalak’s rule, as he increasingly directed all of Tyr’s resources towards the completion of his ziggurat, the nobles who met and discussed options proposed several possible post-Kalak solutions, among them a new monarchy (with a king chosen from amongst them) and a paternalistic oligarchy. The circumstances that surrounded Kalak’s assassination meant that these were cast aside as Tithian took the crown.
The Turax noble family is a strong proponent of implementing a conservative oligarchy. Some nobles, such as the Asticles family, have more progressive views, possibly entertaining a bicameral system involving elections and the common folk. The Mericles and Beryl families are strongly monarchist, as are (generally speaking) the common folk of Tyr, who are Tithian’s strongest supporters.