Well, in 1905 France and Germany almost went at it over Morocco, which both were trying to gain as a protectorate...
So, during the R-J war, but prior to Morocco, suppose Russia formally requested military assistance from France. France declines, not wanting to risk conflict with Japan's ally, Britain. Russia angrily breaks off the Dual Alliance.
When Morocco comes to a head, the Kaiser, rather than backing down as historical, thus feels confident enough to attack France. Britain comes to France's aid under the Entente Cordiale, while Austria-Hungary joins the Germans.
Since they're already at war with Britain, Germany promises to aid Russia in the Pacific if the Russians declare war on Britain. The Russians do so; whether they declare on France is another matter.
Serbia and Belgium come in with the Entente Cordiale. Italy attempts to stay neutral or allies with France and Britain - her more recent treaties with France historically undermined her presence in the Triple Alliance.
Turkey could be a wildcard; Britain would want Turkey to cut off Russian access to the Med, but also has issues with Turkey over massacres of the Christian population just seven years earlier. Turkey might also be reluctant to oppose allied A-H and Russia - or, their combined threat might be enough to have them side with Britain.
Anyway, the line up looks like:
Britain
France
(Italy)
Japan
Belgium
Serbia
Germany
Austria-Hungary
Russia
If you really want to upset the cart, get the Americans involved after they lose merchant ships - to a British blockade of Germany and Russia. That'll help even things up a bit.
It's a suggestion. I don't guarantee that it's all plausible.