Well then, how do you get competition introduced to China? We can't just butterfly away the entire Chinese culture of cooperation and and Confucianism and service to the Mandate of Heaven, can we?
The only reason you need competition is to prevent the ability of one man to make a decision that closes off all possibility of certain actions for everyone. Breaking China apart is one way to avoid certain bad mistakes made by some of the Emperors (or very often, the mistakes made by a certain clique around the Emperor that actually governed China). However, that is not the only option.
China's problem begin in the decision of the Ming Dynasty to close off all trade with the outside world and disband its navy. This didn't work in practice. Too many people wanted to trade with China, and too many Chinese wanted to trade as well. In addition, China needed Spanish silver (from the New World) to monetize its economy. It didn't work out like the Ming thought. All that the Ming actually did was undermine governmental authority, encourage piracy, and give foreign powers control of China's seaboard.
When the Ming fell, the Qing continue the policies because as Manchurian horse nomads, they never had a naval tradition and weren't interested in areas outside of China.
One problem for China is, like every great civilization, they think they are completely superior and that no barbarians have anything useful. In many ways, the Chinese were right. China was far wealthier than Europe. Its goods were often of superior quality and cheaper. Outside of precious metals, there wasn't a whole lot that China needed from the outside world.
By the mid 1600s, Europe had eclipsed China in scientific knowledge, but the Chinese never expressed much interest in it. They saw European inventions like the clock and other precise mechanical devices as interesting, but not necessarily important. Furthermore, the main people engaged in this cultural exchange were the Catholic orders like the Jesuits who were trying to find a way to accomodate Christianity with Chinese culture (especially the importance of ancestor rites). When internal politics within the Church sabotaged those efforts, China decisively rejected European learning.
If China was divided, then it's possible at least one of those states remains engaged and reforms earlier.
It is certainly possible for China to be divided. It has a history of having periods of disunity. We just need one to happen right around the 1600-1800s. One possibility is that the Manchu are not able to conquer all of China when the Ming collapses, and other warlords spring up.
In that case, we might have one state based around the Yellow River and North China plain, an independent Manchuria, a state based around the Yangtze and central China, and perhaps minor states based around Canton or Fujian that are maritime oriented, perhaps even one around Szechwan.
Looking for allies, one or some of the states welcomes European traders and eagerly snaps up European inventions. In response, some of the other states do the same. China internalizes much of the new technology and science. It either takes a long time for China to unify, or when it does, the Chinese know enough to feel that the Europeans are a threat and builds up a navy to prject power into the South China Sea and threaten European colonies in the Philippines, Indonesia, and perhaps farther afield.