King Zog is right Fengtian not Zhili.
I think a big important event would be the split of the national assembly sometime in the 1920's. In protest over Shandong, the legislature splits with most delegates protesting by going home putting this in 1922 -1923. The republic is never formally abolished but stays in suspended animation. Technically, the assembly is on recess until it can make quorum.
The British use the suspension of normal parliamentary proceeding to formally delay the handover of Shandong that same year.
This also causes a crisis and a breakdown in the Open Door Policy and the Nine Powers Treaty. The British and the Japanese start informally dealing with the individual cliques, helping them expand and consolidate. The Japanese support Fengtian, and Henan and are generally well liked while the British buy the support of Anhe and avoid the formal abolition of the Republic through their control of the customs revenue. (China under the nine powers treaty which is still in effect leverages a 5% tax. That tax is collected not by Chinese officials, but rather foreign customs officers and is then remitted to the authorities in Beijing. The same treaty grants Japan and Britain among others military access, trade agreements, extraterritoriality, and many other perks. This is why even though the British and the Japanese are encouraging de facto regionalism by arming different generals, they both officially advocate restoration of the republic.)
When the war with the Rice and Grass Movement starts, the delay engendered has proved deadly. The factions they support while regionally strong, cannot act effectively or nationally against homegrown peasant rebellion mixed with anti foreign and slightly anarchist ideals. When the Chinese civil war starts. The British and the Japanese both support the Federalist side for fear of losing everything. They really want to maintain the Boxer rebellion triangle ("the foreigners are afraid of the people, the people are afraid of the government, and the government is afraid of the foreigners") There is a potential for it to split along patronage lines, if it's too successful, not to mention the chance that a nationally sized Chinese state with a modern army might no longer be afraid of the people.
Also Taiwan was taken from China by Japan in 1895 so it's unaffected by this timeline and remains a Japanese colony.
Names and exact timelines will have to wait until the weekend.
The more I think about it, I neglected something important. There would have to have been a huge diplomatic fallout between Britain and America over Shandong. The Americans were ones who forced the Japanese to give it back at the Washington Naval conference but if the British don't, that could mean a huge difference in the Pacific balance of power as the alliance between the two is broken. A weaker Japan then changes from a threat into a tiebreaker with both a the Americans and the British trying to keep the Japanese support in the Eastern Pacific.