Traditionally the old style Monarchies Germany, Austria-Hungaria and Russia were more closely related to eachother than to one of the more western European States, as all were rather Ancien Regime and less democratically developped than the West. So on this base, they technically coudl get well along, if focussed on the social agenda only.
On Nationalistuc motives, the Slavisch Rusian Empire was an archenemy of both A-H and Germany, who were mostly multi-ethnic, but dominated by the Germanic people. This Nationalistic attitude also made France a likley opponent to the German and A-H Empire, as France was more or less a National State, compared to the more multi Ethnic neighbours. Italy was questionably the same, being not truly national state, but roughly made up of a more European orientated North and a more Mediteranean orientated South. The UK were left outside this, being traditionally much more Liberal towards minorities.
So the proposed German-Rusian-Italian Alliance is not possible, as two archenemies are not going on well with eachother and Italy is a serious uncertain factor (as it also was in the OTL). A-H and France could not get well with eacother for simmilar reasons, besides both laying claims on being the leaders of their alliance as well, making it a serious competition. The UK could tie up with any state, or alliance, except with Russia, which was considered a liability and a contender in colonial affairs. (Also France, but to a somewhat lesser sence, as France did not threaten the UK's primary colony India, which Russia did by claiming Perisa and parts of today's Afghanistan and possibly Pakistan.)
So an Alliance between a German orientated Coalition of Germany, A-H as a core, could more likely be supported by the UK, Italy and possibly some lesser states, while the block around Russia was more likely to be supported by France and possibly some minor states as well. That would be the core for any alliance forming in the pre WW1 period.