Three way wars, as a rule, don't work because two sides find some common ground and either set aside differences until war is over or actually all to bring third side down.
A party to the conflict can also be on two sides at once. The Syrian Civil War is a fun example of how weird war can get. It's ostensibly a three-sided conflict: the Syrian regime opposes the Opposition, the Kurds, and ISIL/ISIS/Daesh; the Opposition and Kurds oppose the regime and Daesh; Daesh opposes everyone. That's the official line. However, in the northwest of the country, the regime and Daesh have something of an understanding as they both fight the Opposition and the Kurds (the regime kind of helps Daesh here); in the east, the regime has a similar understanding with the Kurds as they battle Daesh.
I can't imagine how Russia and Germany going communist would lead to a three-sided conflict though. If Germany, one of the biggest industrial powers in the world, and Russia, an emerging power at the time, turned communist and allied, Britain, France, and every other country would lose their shit and probably find some way, together, to try and squash the revolution. This happened during the Paris Commune in 1871 -- Prussia actually released French POWs to help them fight the Communards.
Here's an idea:
World War I as we know it doesn't occur. The Ottoman Empire lives on, for a while, but then Russia starts pecking at them. Like during the Crimean War, Britain and France come in to "help" the Ottomans. They help a little too much, pissing off the Ottomans, and it turns into them fighting everyone, Russia fighting Britain/France, and Britain/France fighting Russia.