Survival of the Southern Song

I was thinking of Making a timeline about the Survival of the Southern Song Dynasty.

What is needed for the Southern Song to survive?
 
The Mongol Empire has to collapse after conquering the Jin and before invading the Song. Maybe if the Black Plague kills Chinggis and abunch of the Mongol Royal Family.
 
The Mongol Empire has to collapse after conquering the Jin and before invading the Song. Maybe if the Black Plague kills Chinggis and abunch of the Mongol Royal Family.

But is it possible for Yuan and Southern Song to coexist?
 
I suppose you could have Southern Song set up on Taiwan or Luzon and wait out the Yuan dynasty. Koxinga's son lasted 20 years on Taiwan. This will require holding out for a century. Pretty hard to pull off.

Then again, the Ming dynasty was in some ways a Southern Song revival under a peasant family. Perhaps someone with the right bloodline comes to power instead.
 
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