While the Quadruple Alliance of 1815 is the most famous and important, two other European
"Quadruple Alliances" are still relevant
to modern historians
The first Quadruple Alliance, ratified on August 2nd, 1718 and consisting of Austria, Great Britain, the Dutch Republic and France, was formed to prevent Spain from taking Sardinia and Sicily from Austria and Savoy respectively. Philip V of Spain backed down after French troops invaded Spain and the British fleet carried Austrian troops to Sicily, signing away his claims with the "Treaty of the Hague".
1813-1815 saw the formation of the second Quadruple Alliance. This time Austria, Great Britain, Prussia and Russia got together to establish sustainable peace at end of the Napoleonic War. The treaty was reasonable successful, leading to the Concert of Europe (a long period of relative peace in 19th century Europe).
The third "Quadruple Alliance," signed on April 22nd, 1834, called for Britain and France to help liberal (as opposed to conservative) claims to the Spanish and Portuguese thrones. Specifically it helped Maria Cristiana win the first of the Carlist Wars and Maria da Glória win the Miguelite Wars.