What would you call a monarchist government where multiple families rules in turns?

I'm making a fantasy novel. In this one there is a monarchy system, where 4 families rule in turns. After the current monarch dies, the next family in the circle most present an heir from their family to ruse the nation until they die and then the next family takes the throne.

What would you call this government model? Oligarchic monarchy? Poli-Monarchy? Help me with some suggestions. I'm also not sure if this has happened in the history, I can't find anything about it.