Of course, there is one multi-national entity that no longer competes as such for the simple reason that it no longer exists: the Union of Soviet Socialist Republics, which more often than not topped the medal standings once they entered the games in Helsinki in 1952 with the Cyrillic abbreviation "CCCP" emblazoned on their uniforms. But if the constituent elements of the dissolved Soviet empire are toted up in the aggregate and added to Russia's independently strong showing, the medals title would be theirs once again. With 23 golds, 19 silvers and 40 bronzes, for a total of 82 medals tallied by Ukraine, Kazakhstan, Belarus, Azerbaijan, Georgia, Lithuania, Uzbekistan, Armenia, Latvia, Estonia, Tajikistan and Moldova, the once and no longer USSR could claim a total of 164 medals (47 golds, 44 silvers, 73 bronzes) far in front of the United States's total 104, and also edging the US in golds 47 to 46. Not too bad for a region that is habitually portrayed as struggling with political dysfunction and economic instability. But whatever Vladimir Putin's neo-imperial ambitions for his truncated Russia, we won't be seeing any such reassembled sporting empire, whether branded "CCCP" or not.
What of the showings made more "relevant" and up-to-date multi-national entities? The Arab League and African Union (whose memberships somewhat overlap) would not make much of a mark in the medals tables if competing as units, with 33 medals (11 gold, 12 silver, 10 bronze) for the African Union and only 12 (2 gold, 3 silver, 7 bronze) for the Arab League. The 27-member European Union fares much better, with Great Britain, Germany, and France (a notably well balanced 34 total medals, 11 gold, 11 silver, 12 bronze) leading the way to a dominant overall EU haul of 305 medals—almost 150 ahead even of a mythically reconstituted Soviet Union and nearly three times that of the non-mythical United States—92 golds, 104 silvers, 109 bronzes. But before announcing that we are entering into a renewed European Era, limiting the tally to the 10-member Eurozone—which has, of course, carried the cause of a truly united Europe to its greatest extent, and paying a stiff economic price for doing so—reduces that result to 154 total medals (40 gold, 58 silver, 56 bronzes). And it has to be said that the ejection or withdrawal of Greece (2 bronzes) would hardly register on this Olympics balance sheet at all. And ditto Portugal (1 silver).
Finally, what of the "BRICS," the omnipresent (in punditry at least) specter of a Brazil, Russia, India, and China poised to overturn the Euro-centric economic order that has ruled the world ever since Vasco de Gama rounded the Cape of Good Hope in 1498? Well, Russia is holding its own and China is moving ahead, but India was a bust in London (6 medals total, 2 silver and 4 bronze) and Brazil (17 medals in all, 3 gold, 5 silver, 9 bronze) was no threat to the established sports world order. With the 2016 summer Olympics in Rio, perhaps a host country bounce will push Brazil up the medals tables. Added to Russia and China, a resurgent Brazil may yet make the BRICS an athletic force—assuming that anything can be expected from India.