Gloss, it is possible to break China apart into different Chinas, but at this point it is going to be exceedingly difficult for you to break China into different nations. Tibet and the Steppe, sure. Yunnan? Maybe. More? Unlikely.
To make an analogy that is illustrative, yet deeply flawed, imagine you are talking about 12th century Europe and you are asking us to tell you "how can we bring back Hellenism and other Pagan religions?" You'll get people telling you it might be possible in the northernmost fringes of Scandinavia, parts of Eastern Europe - Particularly Lithuania, and maybe Russia. Or for another, what parts of the Middle East can be made Christian again?
When we discuss China, the political unit is irrelevant. We are discussing a cultural, political, and social identity that defines how individuals see the world. That they spoke different languages meant nothing to that broader identity, and much like Latin or Classical Arabic united Catholic Europe and the Middle East, literary Chinese united China. But, unlike those two areas, the very existence of two emperors is an afront to the existence of another. To be Emperor meant to be Emperor of China, not such and such a place. If you want to break China and what it means to be Chinese, you need to start earlier with the Warring States, or with the Han. By the time of the Tang its almost too late, and certainly be the Song it was.