"This is now threatening the heart of Europe and the core of the European project," Guy Verhofstadt, the former prime minister of Belgium who now leads the Liberal group in the European Parliament, told AFP.
The refugee crisis is "deeper than the euro crisis. I think it's a real test -- it's also an opportunity to make a jump forward," he added.
The perfect storm of crises has in recent months brought to the surface divisions that have long been papered over in pursuit of a union of 28 nations and 500 million people, together the world's biggest economy.
A deep rift between eastern and western EU states on migrants has been added to the split between north and south on the eurozone debt crisis.
- Refugees, euro -
Instead of solidarity and humanity in dealing with thousands of migrants dying while trying to flee Syria, Afghanistan and Iraq, the world has been treated to the unedifying spectacle of EU leaders bickering over asylum quotas amounting to 0.032 percent of the continent's population.
The result is that one of the EU's most cherished ideals -- the Schengen passport-free area, a continent without borders -- is now at risk as countries reintroduce border controls and build razor-wire fences.
The migration crisis has come on top of a debt crisis in the eurozone that has left some of southern European members economically devastated -- piling misery on the same area that, incidentally, has received most refugees.
While debt-laden Greece finally got a huge bailout after months of bad-tempered negotiations, analysts say many of the single currency's underlying problems remain.
Whichever government emerges from Sunday's Greek elections, the country's colossal debt is probably unsustainable, while broader talks in Brussels on increasing banking union have largely stalled.
Add the crisis in Ukraine that has plunged relations with Russia to their lowest point since the Cold War, and the looming threat of a possible British exit from the EU in a referendum due by 2017, and the problems mount.
Monnet -- the Frenchman who became the first head of the European Coal and Steel Community, the forerunner of the EU -- believed that Europe would be the "sum of the solutions adopted for those crises", but solutions are exactly what leaders are failing to provide.
Governments are increasingly paralysed, with many of them looking over their shoulder at populist parties from both the right and left wing.
- 'Integrity under pressure' -
Together, the crises are increasing the likelihood of countries acting unilaterally to protect their borders or their economies from disruption -- thereby undermining the whole point of the EU.
"Crisis is piling up on crisis. The EU's integrity, if you look at Greece or Schengen, is under pressure," Janis Emmanouilidis of Brussels-based think tank the European Policy Centre told AFP.
European Commission chief Jean-Claude Juncker recently made an appeal for "more Europe", echoing calls across Brussels for greater integration to keep the bloc's core ideals in place.
However Raoul Ruparel, co-director of the Open Europe think tank based in London, said the "confluence of very serious existential crises" required urgent reform in Brussels.
"Trying to force all these countries into one size fits all has worsened the divisions. The eurozone showed that with Greece and Germany, now we are seeing that with the migration crisis between east and west," he told AFP.
"You have this combination of institutional flaws undermining the policy, and then pitting the member states against each other -- that combination is toxic."
But the EU has not yet reached its "Titanic moment", the EPC's Emmanouilidis said, pointing out that the past 60 years of integration on a once-warring continent had produced a "collective DNA".
"It might be the end to some elements of the EU, but I don't think the EU itself is going to under," he said.