How did Malaysia resolve its PM crisis?
The King called every MP in to his palace. Sat with them one by one. No group meeting. For 3-4 minutes. Asked who he supports? Tallied the result. And made the one that received the highest support the Prime Minister.
Being practical and people minded.
Though that's not the end of the story as he still will need vote from majority of MPs. But a good on the spot resolution nevertheless.