WI: More Aggressive Song Dynasty?

How would you make the Song Dynasty, one of the most culturally achieved dynasties in Asia, more aggressive to the point where it can fend off the Mongol Hordes?
 
It's a tough one; one of their major problems was that they never came up with a way to acquire a decent source of cavalry, which made offensives almost impossible for them.

The Qing and Tang found ways around this, but the Qing had Manchuria and were better able to assimilate Mongolians than the Song ever were. The Tang had sources available that the Song simply lacked.
 
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