The problem with this time period, imho, is that it coincides with the height of "yellow journalism" over much of the Western nations. Even if the Tokyo, Paris, London, et. al. don't want to rock the boat, the newspapers in Europe and the US will be full of atrocity stories--heathen Chinee slaughtering white woman sells papers, you know. So I think if the legations are sacked and the many thousands of foreigners are murdered, there will be a lot of public pressure to do something. Look at the example of the Indian "munity" in 1857: a lot of the educated elites wanted a measured response, in order not to alienate common Indian opinion any more than necessary. Queen Victoria herself spoke of the need to punish only the rebels, in her words, to show "that there is no hatred of a brown skin". But soldiers on the ground, and even many of the officers, would indeed respond to Indian atrocities with atrocities of their own. One hears of widespread summary executions of Indian adult males in a given area, or of forcing Indian prisoners to lick up the blood off of floorboards with their tongues, prior to their own executions. If the sense of Western outrage is much higher here than in OTL, you may see more Chinese dead, too.
What Zmflavius says is true: the various imperialist powers tended to prefer a decrepit Qing Empire, that would honor the various agreements, over anything that risked setting up a new government that did not. However, that still leaves the question of the role of court politics in allowing or even encouraging the rebellion. The support given to the Boxers in OTL was bad enough. If more support is given, or the Boxers are simply much more successful in the original run, then I think you might see some broad interference in court affairs behind the scenes. This would not be in order to extract more concessions (although that may happen as well), but primarily to prevent another such uprising. If the Europeans can find a way to agree on who (a big if), I think you could see the installation of more Western "advisors" to the throne, for example. You might also see the creation of a new, modern-style palace guard under Western instruction. The Empire of Japan trained the Korean palace guard after 1895, which was quite effective at increasing their control over the government in a fairly non-obtrusive way.
I agree with those that say true partition--along the lines of the Scramble for Africa--is unlikely. After 1897 in OTL, the Germans did set off a mini scramble for China, but it took place under the Qing Empire. and I think the powers will be more than happy to see it continue, especially if it can be made more pliant. Of course, huge indemnities will go a long way toward smoothing things over. It's possible that we would see more concessions. However, if this happens, I assume it will be less "old-style" concessions--e.g. actual tracts of land for naval bases and traders, and more "Nishihara Loan" style concessions--e.g. Japanese companies are the only ones with the legal right to operate coal mines in Manchuria.