WI: Carolingian Capetian-style dual kingship

The Capetian dynasty tended toward dual kingship between father and son, allowing de facto primogeniture. Could the Carolingians have done this?
 
It's possible but difficult. The appanages that the Carolingians would give out to second/third/fourth sons are practically empires of their own, making conflicts between sons more likely.
 
This wouldn't actually be as difficult as it might seem. Early Capetians did tend to crown their heirs as co-kings. I know Louis VI crowned his son as his co-king in...1129, and Stephen I of England attempted to have his own son crowned as his co-king during the Anarchy in the Capetian custom. I don't know why they stopped doing this, but I assume either strife between father and son or that as the law became more defined and respected, the heir succeeding the king was simplified to the point that crowning the heir as co-king became unnecessary.
 
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