Is there such a thing as an oligarchical monarchy?

The main setting of my fantasy novel series is set in a fictional version of North America. The land is home to most of these Mages with Angel powers (still thinking of a proper name),whom the world is convinced no longer exist but have simply went into hiding, living in large village they've built the mountains. I was thinking that they would love in a sort of hybrid of an oligarchy and a monarchy,in the sense that they would appoint a suitable person to be chieftain and,if the person is shown to a reliable and competent leader,their children would be allowed to inherit the responsibility. If not,they would be completely stripped of their title and the title for Chief would go to someone else. The Chief would create laws and make decisions, but the elder council would have the final word on whether these should be passed or not. Would this be possible?