BRUSSELS (Reuters) - Four great crises around Europe's fringes threaten to engulf the European Union, potentially setting the ambitious post-war unification project back by decades.

The EU's unity, solidarity and international standing are at risk from Greece's debt, Russia's role in Ukraine, Britain's pursuit of opt-outs and Mediterranean migration.

Failure to cope adequately with any one of these would worsen the others, amplifying the perils confronting "Project Europe".

Greece's default and the risk, dubbed 'Grexit', that it may crash out of the shared euro currency is the most immediate challenge to the long-standing notion of an "ever closer union" of European states and peoples.

"The longer-term consequences of Grexit would affect the European project as a whole. It would set a precedent and it would further undermine the raison d'être of the EU," Fabian Zuleeg and Janis Emmanouilidis wrote in an analysis for the European Policy Center think-tank.

Though Greece accounts for barely 2 percent of the euro zone's economic output and of the EU's population, its state bankruptcy after two bailouts in which euro zone partners lent it nearly 200 billion euros ($220 billion) is a massive blow to EU prestige.

Even before the outcome of Sunday's Greek referendum was known, the atmosphere in Brussels was thick with recrimination - Greeks blaming Germans, most others blaming Greeks, Keynesian economists blaming a blinkered obsession with austerity, EU officials emphasizing the success of bailouts elsewhere in the bloc.

While its fate is still uncertain, Athens has already shown that the euro's founders were deluded when they declared that membership of Europe's single currency was unbreakable.

Now its partners may try to slam the stable door behind Greece and take rapid steps to bind the remaining members closer together, perhaps repairing some of the initial design flaws of monetary union, though German opposition is likely to prevent any move toward joint government bond issuance.

The next time recession or a spike in sovereign bond yields shakes the euro zone, markets will remember the Greek precedent.

DESTABILIZING

An economic collapse of Greece, apart from the suffering it would cause and the lost billions for European taxpayers, could aggravate all three of Europe's other crises and destabilize the fragile southern Balkans.

With tension already high in the eastern Mediterranean due to civil war in Syria, the eternal Israeli-Palestinian conflict, the unresolved division of Cyprus and disputes over offshore gas fields, a shattered Greece might turn to Russia for help. In exchange, it might veto the next extension of EU sanctions against Moscow, or even offer access to naval facilities once used by the United States.

Athens is already struggling with an influx of refugees from the Syrian and Iraqi conflicts who wash up on its Aegean islands, seeking the safest transit route to Europe's prosperous heartland in Germany or Sweden.

Cash-starved Greek authorities are more than happy to see them head north in search of asylum elsewhere in the EU. It is not hard to imagine a government cast out of the euro zone using migrants as a means of piling pressure on EU countries.

The "boat people" crisis has proved divisive in the EU, with Italy and other frontline states accusing their northern and eastern partners of lacking solidarity by refusing to co-finance or take in quotas of refugees. Britain has refused to take any.

Failure to resolve Greece's debt crisis after five years of wrangling makes the EU look weak and divided in the eyes of Russian President Vladimir Putin, Chinese President Xi Jinping and others looking to expand their power.

Brussels officials acknowledge that the euro zone crisis has caused a renationalization of decision-making on some policies and sapped the "soft power" of Europe's model of rules-based supranational governance. It has weakened the EU's hand in world trade and climate change negotiations.

Worse may yet be to come.

Britain's demand to renegotiate its membership terms and put the result to an uncertain referendum by 2017 raises the risk of the EU losing its second largest economy, main financial center and joint strongest military power.

Despite opinion polls showing British supporters of staying in the EU have roughly a 10 point lead, and some relief that Prime Minister David Cameron did not include any impossible demands in his renegotiation agenda, there is nervousness in Brussels.

UK opinion polls got the May general election spectacularly wrong. Since his victory, Cameron has been tripped up several times by Eurosceptic rebels in his Conservative party.

A long, agonizing Greek economic meltdown, whether inside or outside the euro zone, with social unrest and political havoc, might reinforce those who argue that the UK economy is "shackled to a corpse".

Given Russia's lingering Cold War hostility toward Britain, seen in Moscow as the United States' most loyal ally, Putin would likely be delighted by any prospect of the UK leaving the EU.

It would weaken those in the EU seeking a robust response to Russian behavior in Ukraine and Georgia and detach Washington's trusty partner from the continental bloc, although Britain would remain a member of NATO.

That could strengthen Putin's hand in dealings with German Chancellor Angela Merkel, who has led European diplomacy seeking to restore Ukraine's control over all its territory.

Rem Korteweg of the Center for European Reform compares the interlocking crises to the four horsemen of the apocalypse in the New Testament Book of Revelation: harbingers of a "day of judgment" representing conquest, war, famine and death.

"The EU's leaders will find it hard to tame these four horsemen," the Dutch thinker wrote in an essay. "If a European answer cannot be found, the horsemen will continue to promote chaos, instability and mutual recrimination within the EU."

(Editing by Ruth Pitchford)