Indeed: that's the paradox here. The simple fact is this scenario requires the UK, US, or Germany to be, international politics speaking, in two places at once so interests overlap in a way that produces the alliance structure. Germany, by nessecity (both in it's positioning and the requirement of the scenario to be against France and Russia) has to put the lion's share of its attention on the Continent (See Bismark's Map of Africa comment for the spirit of that principal), while the US is for no shortage of reasons turned inwards on the Western Hemisphere. Thus, you need a UK who feels they need to stick their fingers in both those pies and feels confident in it's ability to do so, while simutaniously seeing Germany as sufficently more threatening than France or Russia to be willing to actively push for a situation that would increase those nation's position. That's a very, VERY narrow window of difference in power distribution, especially if we assume US and German industrial prospects of anything like the pattern that's been taking off in both since essentially the 1840's.
However, I assume we have to push the POD at least post-Unification, which essentially traps us with South Europe and the Pacific as the main zone of political-economic flexibility. Hence the Italians, Austrians, Japan and Ottomans being the main nation's who's metaphorical "weight" and alignment we can work with. Taking Japan out of the equation as a power might also help here: East Asia being a bone of contention between Britain and Russia. Feeling obliged to concede northern China,Korea, and Japan to Russian influence to secure India due to lacking a viable regional counterweight would pull Russian investment and expansionist interests eastward and into Siberian development , reducing pressure on the Ottomans and allowing the resurgance to occur (perhaps by the British feeding the capital and expertise that otherwise facilitated Japanese crash development into the Caliphate?). Combine that with butterflies that produce less development and greater internal strife in AH: maybe the result of a "Great Game" between France and Germany in the Balkans as the former seeks to undermine German's ally and earn the good will of and strengthen Italy as a baton to wave at their rival's southern flank,and Germany is propping up it's one big remaining friend, and you could have the OE and Austria in a contest as Russia bows out of the regional contest. Austria backs a Serbian client regeime and Greek ambitions, French and Italians promote the Croats and Tyrolian/Istrian Italians, Ottomans get Bulgaria to stay loyal and Romania to align with them, and all the while the Magyars get surlier and play everybody off one another to pry out greater concessions by either providing or withholding concent for certain reforms and actions on the part of the common Imperial adminstration.
Now, the US would have to be dragged in somehow... how about over Japan? If we hamstring Meiji's reforms, given US Pacific interests I could see them trying to integrate the islands into the informal commercial Empire. Way more profitable than the Phillipenes. If Russia has been given carte blanche by Britain in China, we could easily see Washington and St. Petersburg relations go as cold as both ends of the Bering Strait as the former tries to get a Open Door where the Czar has locked it down tight, while Russia will resent the US for pressing into Japan which they thought was "There's". Add in the vast difference in the political cultures and the influx of immigrants to the US from those Eastern European nations under Russian oppresion (Poles, Lithuanians, ect.) in the late 19th/early 20th century and have them integrated into the Irish American parts of the Democratic political machines, and I could see that party adopting a Anti-Absolutist/ Wilsonian Idealism plank a little earlier, especially if there's no "American Empire" formally as a result of no Spainish-American war (Or, maybe just one with no territorial gains and the territories freed into self-government) that could lead to more activist Monroe Doctrine idea to move just from "No new European influence" to "European influence must actively be removed from our Hemisphere. Venezuelan dispute than has a reason to boil hotter, maybe even having the US expand it to the question of the Falklands and Belize.