With a PoD of 1873, have the League of Three Emperors (with OTL Germany, AH, and Russia) go to war with major Democracies, and have this conflict become known as WWI.
For added twists, if you can create a scenario where either side can win.
In 1873 Alexander II, while heading to the rooms occupied by his mistress, Princess Dolgoruki, slipped on the stairs, fell and hit his head. When he got up, he was a different man: slight concussion greatly improved his mental abilities (change to the worse was almost impossibility so here we go ...).
One of the 1st things he did (after returning from Dolgoruki, first things first) was to order construction of the Black Sea fleet. Then followed orders to raise import taxes and to find somebody competent to change existing contracts with the railroad companies (young Protege of Minister of Ways and Communication, certain Sergei Witte, proved to be an incredibly successful choice). While he retained for a while his Chancellor, Prince Gorchakov, he started having his own ideas regarding Russian foreign policy.
In 1875 Russian government refused to support the British diplomatic effort to prevent the looming Franco-German war: France was recuperating from defeat of 1871 too fast for Germany’s taste and there was a serious discussion in Germany about launching a new war; as usually, the Brits were trying to resolve the problem by sticking somebody else’s neck so The Russian Chancellor Prince Gorchakov (who was more than a little bit obsessed with an ideas of the “European Concert” and keeping the Brits happy) had been approached with a request to apply some pressure on Berlin. However, to everybody’s surprise, Alexander II refused to follow his advice and assured Bismark and German Emperor that Russia is not going to act contrary to the German interests. Of course, with any other monarch this decision would be expected because memory of the CW was still alive and neither France nor Britain were acting as the friends of the Russian Empire since. However, Alexander and his Chancellor had been consistently confused in their foreign policies and the British appeal would have all chances to succeed if not that obscure incident of 1873.
Of course, courtesies of such a magnitude are not coming for free so the deal had been made regarding potential Russian interests on the Balkans. Germany, AH and Russia forced the Ottoman government to guarantee that no warships of the countries that do not have borders on the Black Sea would not be allowed to go through the Straits at the time of war. In exchange, Russia guaranteed that there is going to be no military involvement on behalf of the Ottoman Slavic subjects providing there is a guaranteed autonomy of Bulgaria (which should be demilitarized). AH was granted some administrative rights in Bosnia and Herzegovina. Slavophiles in Russia went berserk but Alexander was unmoved declaring that the most noisy individuals may chose between shutting up, going to fight as volunteers (at their expense) for the “Slavic cause”, or to be resettled in the Siberian governorships (transportation expenses being paid by the state). Surprisingly, the 1st option proved to be the most popular one.
As a result, in 1876 Germany went to war against France with AH and Russia declaring war as well (just as a show of solidarity, however it was agreed that the help would be sent if required). After German troops passed through Belgium Britain declared war on Germany and its allies thus making the whole affair “global”. The British expeditionary force proved to be inadequate for changing situation in France even without Russian and Austrian involvement. Within 6 months France capitulated. Attempt to evacuate BEF was only partially successful and most of it was surrounded and forced to capitulate at Dunkirk. For a while Britain continued a naval war but without any significant effect: most of the German, Austrian and Russian ports had been adequately defended, none of these countries was seriously dependent upon the overseas trade and their combined resources would allow to stay at war forever. With the Ottoman Empire and Italy remaining neutral fighting on European continent was over. There were few obscure military encounters in the Central Asia (mostly involving British-led Afghan bands) but they did not produce any noticeable results.
The US remained neutral (even if we consider the US of that time as a major Democracy, its involvement in European war requires ASBs).
Formally, the war kept going but within a year it became clear even to the British politicians that it is not going anywhere. Copenhagen had been chosen as a site for peace talks and soon enough the WWI was over.