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In the middle of the 11th Century the glorious and esteemed Caliphate of Cordoba came to an end when the Caliph fled the city and the state fractured into independent taifa states that proceeded to fight amongst each other until conquered by The Almoravids. Unique amongst them was Cordoba which lasted from 1031-1091.
You see following the flight of the Caliph the city was left leaderless and so Sheikh Abu I' Hazm who invested in legislature and judiciary counter balances to his power. He considered himself the 'Custodian' of Cordoba and the practices of a 'Collective Leadership' or probably 'Ogliarchy' continued under his son Abu I' Walid. It was only when Abu I' Hazm's grandson began to fight and take power from the other government functions and nobles did things go downhill and lead to the Emir and take over by Seville. Then the Almoravids came.
Granted this experiment in Italian City-State like republicanism is on a timeframe I wonder if the practice could spread and survive? Specifically for Cordoba the hinge is the nobles stepping in on the grandsons and breaking the hereditary nature of things. The other would be coups within the Monarchial Taifa states against Monarchial styles of government.