What happens if different factions within the congregation each appoint their own Imam after the original Imam breaks purity?

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If each group within the followers appoints their own Imam and prays behind them, the analogy of the madhhab (school) and the position of al-Shafi'i suggest this is permissible. This is because the followers have the right to pray individually, which analogously allows them to appoint a leader, just as they could at the start of prayer. It is also valid if some pray behind an appointed leader while others pray individually.