There are many possibilities.
I don't know enough about the post-Xin and pre-Eastern Han era to comment, but I have read that Emperor Guangwu (the first of Eastern Han) was a very competent military commander, so much so that he drafted plans for his generals and expected them to follow them in detail and they actually worked, one of the few times in history a monarch micromanaging the military ends well. If Guangwu had been butterflied away somehow (perhaps died of a freak accident or illness), what else could happen? I have no idea.
I hear that the Three Kingdoms era is not very plausible, as all three rulers are focused on reunifying the Han state and thus would go to extraordinary lengths to do so rather than settling down to rule their own realm. I don't know enough to affirm or contradict that.
The most obvious place to start would be the post-Jin era, which was extremely turbulent. If you wanted a two-state order, you could go with a Tuoba state in the north and a semi-Han semi-indigenous people, such as the order between the Tuoba Wei and Liu Song, which lasted for sixty years. Instead of having the Northern and Southern dynasties period end with the Northern Zhou being succeeded by the Sui and conquering Qi, Liang, and Chen, you could have a sort of north-south equilibrium emerge in which each state recognizes the other, sees itself as legitimate and the other as barbarian and different, and thus would rather leave the other state be rather than risking ruinous conquest. The border I most often see in north-south orders is the Huai river. A multi state order might be more difficult to construct. It would require knowledge I don't have, but I still believe there is a possibility that the Sixteen Kingdoms period could result in at least two or three states besides the Eastern Jin: one based in Shu, one based in the northeast (perhaps with Jinan or Ye as a capital), and one based in the northwest (with Chang'an as a capital).
I don't know enough about the Sui-Tang transition to make intelligent comments there except that I hear it was pretty devastating and not to be underestimated.
The 5 Dynasties and 10 Kingdoms is an area I know about, however, and I do happen to know a bit about them. I've read that some historians compare the Tang collapse and post-Tang era to the collapse of the Frankish Empire, which has, IMHO, at least a few similarities among many differences. Though the southern states were the most divided, they actually had a pretty stable existence through that period: Shu was briefly conquered by the Later Tang but quickly regained independence and the Wu were replaced by the Southern Tang, but otherwise, states like these as well as those like Southern Han, Chu, and Wuyue were stable enough. The North, though united, was far less wealthy due to continued warfare and the machinations of the Liao during the Later Jin and Later Han. Perhaps if the Liao are successful in their occupation of the North, which was too difficult for them to swallow IOTL in any case, the north will effectively be neutralized and the south will be able to build itself into independent and defensible polities. Not until the Later Zhou did the rulers of the north see themselves as Han and grow strong enough to make inroads against the south and against the Liao.
It's arguable that the Song period was one of a "disunited China". The Liao and Xi Xia were contemporaries of the Song, and the Liao especially humiliated the Song by asserting a dominant "elder brother" status and demanding tribute. The Jinn that conquered the north humiliated Huizong and Qinzong after the Jinkang incident and were seen by many, including the Mongols, as the legitimate successors to the Mandate, and the name "China" or "Cathay" is thought by many to have come from Qidan, or Khitan, the ethnicity of the Liao. Thus, it is best to see the Song-Liao-Jin period as a period of disunited "China".
After this period things become more difficult as my knowledge on these matters peters out. I will mention that the Mongols technically claimed still to be the "Northern Yuan" and repeatedly defeated the Ming (see Tumu crisis), and so could be called a "Chinese" successor state at a stretch. Other than this, however, it seems kind of difficult, as there is such a tradition of unity. Perhaps an ideological divide like the Communist-Nationalist divide?
What drives me nuts is when people say "China's unification was inevitable". Prove it. Reason says that when you make an assertion, you have to prove why it's true, rather than forcing me to prove that it's not true. What I can say to claim that China's unification was not inevitable is that there were long periods of disunity and that many Chinese states have recognized the legitimacy and even ascendancy of one another for decades and even centuries. I know that the human and resource cost of conquest is immense. Just look at the population decrease during the Three Kingdoms period. Yes, I know it doesn't mean tens of millions died necessarily, some could be off the record due to poverty so extreme they were forced to evade government taxation. But the fact that the majority of the Chinese population perished during that time or was driven to destitution, during a time of sixty years of near continuous warfare, points to the enormous cost of unification. If the three states had settled and acknowledged each other and made peace, might that have saved lives and resources? It's a question that should not be answered lightly or spuriously. And that's just one example. Unfortunately, I don't have time to say more.