Have the Russian military prepare more options for mobilization BEFORE the war. OTL, Germany jumped in partly because Russia mobilized everybody, not just units near A-H.
Have e.g. Romania be prepared to let Russian troops transit through to Serbia, so Russia is more visibly defending Serbia than attacking A-H.
Have someone in Germany sit on Kaiser Willy once they realize what a Charlie Foxtrot this was going to end up being, and send a strong (private) message to A-H to slow down.
Have SOMEONE jump at the chance provided by the British offer of mediation. (Russia and/or Germany probably. A-H won't, but if they get pressure from Germany they might.)
results:
Serbia will be totally trashed, even if they 'win'. A-H will be devastated, even if they 'win'. The Tsar MIGHT get some breathing room for staving off revolution if Russia 'wins'. Of course, the Tsar being who he is, he'd likely squander it, and revolution happens anyway, just later.
German continues to be THE language of many sciences, and the centre of the world chemical industry, for instance.