Is there any plausible path for Germany, France and Russia not to exert their influence and prevent Japan from annexing the Liaodong Peninsula? I
Several.
1) Russia thinks close and thinks small. It piles on against a weak China instead of posing as China's champion against Japan. Basically, while letting Japan keep its gains, it takes a lease over Heilonjiang and Jilin provinces of northern Manchuria for building its Chinese Eastern Railway.
2) Germany, pissed off about the Franco-Russian alliance of the previous couple years, decides it's in no mood to do Russia any diplomatic favors. Without being shown up it's German enemy, France lacks the interest and obligation in sticking its neck out in the Far East for Russia. Russia does not try to intimidate Japan all by itself.
Germany can stay completely uninvolved, or, seek it's own treaty port from China while this is going on - maybe in Qingdao, or maybe further south on the China coast.
3) Britain jumps in first and exerts its influence to prevent Japan from annexing Liaodong, perhaps even it vetoes Japanese occupation of the Pescadores and Taiwan. Germany, France, and Russia don't have anything to do but sit and watch.
If so, what are the immediate consequences likely to be? (I can't imagine Japan retaining the territory to the present day, but how long might it have held it?)
Japan in OTL held Liaodong for 45 years from 1905-1945, so holding it for several decades more certainly seems plausible.
After that, the question boils down to likelihood of Russo-Japanese tensions and war if Russia never contests Japan's hold on Liaodong, and presumably Korea. In my view, for a few decades at least, Japan will see southern Manchuria and Korea as an adequate security zone, and will not see Russia as a threat if Russia is not contesting that. Tokyo won't see Russian activity in northern Manchuria or its hold over all Sakhalin as a problem, so there's much reduced likelihood of a Russo-Japanese war.
If Russia ends up greatly weakening for a combination of European and internal reasons, Japan would eventually seek to move into a vacuum this leaves to the north. But it won't need to force it open by 1905. IMHO.
