Easy to answer. British and French support for an expanded exclusive economic zone in China. My guess is for the UK/France to support the Yellow River basin plus Manchuria is for Japan only. And probably Russia support too.
A Japanese Corp or two could have been bought for the right price.
This could be translated into less Big Power resistance to the Twenty One Demands. That is a modified set of demands on Chinas government would be made earlier and with British support. A modified set of demands that Britain & France could live with would be a gain for Japanese industry and its military position.
Could Japanese participation in Mesopotamia affect Japanese military doctrine and tactics in the future?
The Turkish soldier was not as susceptible to shock and infiltration tactics as the Chinese. Japanese regiments fighting the Turks would have more success with attention to fire power, combined arms coordination, a wider infantry tactical repertoire. At least some of that could affect Japanese Army doctrine in the next two decades. OTL they were not far from implementing similar artillery techniques as the French, or US Army in the 1930s or the British. All this would more so were a Japanese corps to fight in the Balkans, Russian, or Western Front. While Japan had some obstacles in the form of a small industrial plant its possible the doctrine will lead to a infantry division and a corps with higher firepower, and a heavier support tail than OTL. Perhaps better infantry support tanks, & more certainly better MG and other support weapons in the infantry regiment/division.
Aside from actual combat experience there'd be more Japanese liaison/observers with the Entente armies. That could lead to a more balanced view of the capabilities of European armies.