A little bit extra musing here.
1) Mongolians never conquer the Song. Reason? IDK. Eventually establishing a semi-hostile and semi-beneficial trading agreements/ceasefire along the Yangtse. Is this tributary? Vassalage? Does it matter in the end?
2) Corollary: Mongolian attack on Western Europe was stronger, establishes Russia-like subsidiary states in Poland and other east-central nation. HRE is more united than historically with a new clear threat to unite against. May or may not include France. See below.
3) France/English 100 (200?)-years war degraded instead of increased nationalism. Both monarchies collapse in warfare and regionalism (like IRL HRE) expand. HRE may "annex" or "included" these successor states into its organization.
4) Now, everything above is based on an altered Mongolian focus. Stuff after that is a bit more iffy, like if the Japanese will unite the way they did without the Mongolian attacks? We shall assume they did.
5) Zheng he. Ahahaha... no. Pre-black death, the Song (with whatever agreement with the Yuan) turned to the seas, and with their river fleet experience built naval fleets that gained tribute from SE Asia and beyond.
6) Thinking about whether to keep it Yuan/Song, or to "modernize it" as Qing/Ming, or some other combination, like even Ming/Song, or a Qing north and a Yuan south. A United China, though, would be IMHO too powerful for meaningful world politics. It would be like an Anglo-france appearing after the 100 years war that then assimilates all of Iberia.
7) There must be a mechanism for Song inventions (and others) to develop and spread, perhaps against the will of the Song Chinese. Other than the 2 Chinas (maybe a Tibet/East Turkestani State as well) and Japan, I would ideally like a strong and semi-independent Korea and Vietnam, without looking at good Indian states to "buff up". This will give us 4-7 states, or our Portugal/Spain/France/England/Netherlands/Scandinavians "analogies".
*Also, we need motivation. China didn't really WANT anything nonchinese, other than importing horses for the army and silver/gold because duh.*
8) Starting period: a "Chinese Columbus" (Zheng He is too discredited by everyone. I feel dirty if I use that name for this

) finds the New World while Europe slowly recovers from the alt-his 1200-1400 troubles in time for the first East Asian fleets to begin poking about looking for ports. OTL 1492-1520s. This will focus on their exploration and first trading posts and contact.
9) East Asia has marked areas for colonization, and begun pursuing mercantilism concerning trade routes, partners, and puppet states. OTL 1580s-1640s. This will focus on early colonial rivalry and trade-based conflict.
10) "World wars" are fought over colonies and their resources, there are clear delineated "Major" colonial powers, and others who are either scrambling to catch up or to establish a niche. 1700-1750. This will focus on rivalry both over somewhat established colonies as well as puppet states. Major and Minor powers ally for niches, cash, balance of powers and prehaps other reasons.
11) "The Scramble For Europe" As EA heads to modern times, land grows fewer and rivalries intensify. The first directly-controlled colony revolutionalized dealings with puppet states, and soon it became the preferred form of imperialism. Meanwhile, European states have a real chance to play states off each other to try to industrialize a-la japan, despite internal inertia and ulterior motives. 1830s-1860s
I might repost in New NESes. Also, IDK if I will actually run this, but if I do I will run it after Part 2 of The Civil Experiment.