What kind of alternate history would lead to modern China being a federal constitutional monarchy?
I'm contemplating writing a fiction set in modern China in an alternate universe. I have thought about how it would look like, but I need a plausible alternate history that could lead to such result.
Setting
It was the year 2020 AD. China was a federal constitutional monarchy in the alternate universe. Unlike most federations in our universe, its different federal units had vastly different nature, ranging from kingdoms to special administrative regions. In total, it consisted of 3 kingdoms, 2 khanates, 2 republics, 4 special administrative regions and 1 capital district.
Kingdoms
The three kingdoms were located in North China Plain, Yangtze Plain and Sichuan Plain respectively. Among them the kingdom in North China Plain was the most politically powerful. They together made up more than 60% of population. Their heads of federal unit were called Kings/Queens and were hereditary positions. The royal family of the kingdom in North China Plain had a mixed origin of Han and non-Han, while the other two royal families were Han for the most part.
Khanates
The two khanates were located in Mongolian-Manchurian steppe and Tarim Basin respectively. Their heads of federal unit were called Khans and were hereditary positions. 878
Both khan families had a mixed origin of Han and non-Han.
Republics
The two republics were both located in southern China. Their heads of federal unit were called Chief Ministers, who were also their heads of government and were elected positions.
Special administrative regions
Among the four special administrative regions, two of them were located in Pearl River Delta and other two in Yangtze River delta. Their heads of federal unit were called Chief Executives, who were also their heads of government and were elected positions.
Capital district
The capital district was the oldest and the central part of Beijing. It was also called the Old Beijing by the locals. Its head of federal unit was called the Mayor, who was also its heads of government and was elected positions.
Emperor/Empress of China
The head of state on federal level was called the Emperor/Empress of China. Whoever succeeded to the throne of the kingdom in North China Plain was automatically crowned the Emperor/Empress of China. However, in case the kingdom in North China Plain was in regency, the Kings/Queens of the other two kingdoms could act as regents for the Emperor/Empress of China.
Being the monarch in a constitutional monarchy, the Emperor/Empress was largely a ceremonial role and had limited political power. Their most significant power was to appoint the Prime Minister, who was the head of government on federal level.
Republic of Formosa
A.K.A Taiwan. The Republic of Formosa was not under the sovereignty of China, but it recognized the Emperor/Empress of China as its head of state. This was similar to how Canada and Australia recognize the UK monarch as their head of state in our universe.
Question:
What plausible alternate history would lead to the China described above? 274