Well, the Quadruple alliance was:
The United Kingdom
Austria
Prussia
Russia
It was an alliance made to combat France in case they decided to campaign again, like Napoleon did. Weirdly, France did join in 1818, however that was not your question.
The Quadruple alliance (at least this one) was originally started in 1813 with the same members, and renewed in 1815. So no country actually "joined" the alliance in 1815.
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France
France
Italy dropped out of Triple Alliance to fight against the Austria-Hungary in May of 1915, and Germany in 1916.
The Grand Alliance was an alliance made during World War II, which joined together the United States, Great Britain, and the Soviet Union. The United States was led by Franklin Roosevelt, the Soviet Union by Joseph Stalin, and Great Britain by Winston Churchill.
In Europe the British had an alliance with Russia and France called the triple entente and a separate alliance with Belgium. Italy also joined GB later and Russia also pulled out.