BRUSSELS — Europe’s far-right nationalists will have a chance to expand their power in elections for European Parliament that begin Thursday, as they seek a breakthrough that could thwart the workings of the European Union and jolt capitals across the continent.

The once-every-five-years vote is the biggest exercise of democracy in the world outside India, giving the half-billion citizens of the 28 E.U. nations a chance to elect representatives to the European legislature.

Since the last election in 2014, the European Union has been hammered by a refugee crisis, multiple mass-casualty terrorist attacks, a vote by the British people to exit the bloc, a security scare fueled by the Kremlin and a fitful economic recovery following the global financial crisis.

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More so than in previous years, voters will be making fundamental choices about the trajectory of the E.U. The shades-of-gray options that have dominated past votes are giving way to stark decisions over the nature of Europe’s union — or whether there should be a union at all.

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Although far-right and other parties that are hostile toward the E.U. have been on the ballot for decades, they have never wielded so much influence or appeared poised to control such a substantial share of the 751 seats.

“We are ready to say today that the day of glory has arrived,” French far-right leader Marine Le Pen declared Saturday at a raucous rally in Milan, where she appeared onstage alongside anti-immigration leaders from across the continent. “We say no to this immigration that is submerging our countries and that endangers the security of our peoples, our resources and our civilizational values.”

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From grand palazzi in Rome to art nouveau villas in Budapest, Europe’s anti-migration right-wingers have been prepping their battering rams to knock down the doors of the European Parliament. No one expects them to win a majority, but their aim is less to legislate than to obstruct.

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“This election is crucial for the future of Europe and the European Union,” said David McAllister, a center-right German lawmaker who is the head of the foreign affairs committee in the European Parliament. “The nationalists, the populists and the demagogues want to destroy European cooperation.”

The traditional center-left and center-right parties — already struggling last time around — are expected to lose ground to parties further out on the political spectrum.

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“The most important question in the European election is not right versus left — the old, traditional ideological cleavage,” said Peter Kreko, executive director of the Budapest-based Political Capital Institute. “It’s much more important what the mainstream-versus-extreme ratio looks like.”

And that ratio appears poised to change significantly, though not radically, as the vote rolls across Europe through the weekend. Most E.U. countries vote Sunday.

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The biggest shift, according to poll-based forecasts, is that the center-right and center-left political families that have held sway in Brussels are likely to lose their combined majority. The latest projections show them falling from 53 percent of the vote to 42.

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To continue to govern as a grand, across-the-aisle coalition — as they do now — they will need additional partners.

Nationalist and other far-right parties, meanwhile, are expected to rise from about one-fifth of the seats to a quarter. Others, including pro-business and environmentalist parties, are also expected to gain.

The European Parliament has long been a feeding ground, paradoxically, for Euroskeptic politicians. Until recently, few European citizens paid the legislature much attention. Election day turnout is often far lower than for national votes, favoring the passionate extremes who can mobilize their base. And once in office, lawmakers can use generous allowances to bolster their brand and their domestic legitimacy.

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The body’s powers are not sexy. It can’t directly propose legislation, only approve reforms — such as the data privacy overhaul that went into effect last year. National leaders keep major powers around security and foreign policy for themselves. Still, the European Parliament needs to sign off on senior E.U. leaders and the E.U. budget.

This year’s shifts in representation may be relatively modest, but they could have a disproportionate impact on how the E.U. functions, putting the far right in good position to play spoiler.

“Even with a relatively small percentage of the vote, the potential to delegitimize the European Parliament is quite strong,” said Almut Möller, co-head of the Berlin office of the European Council on Foreign Relations. “Brussels is used to operating according to the Brussels consensus. Now the picture will be different.”

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A legislature with less ability to get things done would feed the narrative of the E.U.’s nationalist critics, who argue that the bloc is fundamentally broken. The chaos unleashed by Brexit has calmed demands in other countries to quit the E.U. altogether, but Euroskeptic leaders still want to chop away at its powers and rebuild barriers between countries.

“If your goal is destroying the E.U., then stagnation is a pretty good thing,” said Marietje Schaake, a centrist Dutch member of the European Parliament.

In order for Europe’s critics to wield maximum influence, they will need to work together — something they have failed to do so far.

The far right is now distributed across three separate blocs in the European Parliament, with both personal and policy differences standing in the way of a confederacy of nationalists. One divide is on Russia, since Western Europe’s far right tends to admire the Kremlin while its Eastern European compatriots can be suspicious of Moscow.

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Also stalling the far right’s march are signs that, at least in some places, its moment may be passing.

While nationalists are unquestionably more popular now than they were during the last vote, in 2014, their support in many countries has leveled off as the memory of the 2015-2016 refugee crisis recedes.

In Germany, for instance, the far-right Alternative for Germany party (AfD) is forecast to nearly double its share of the vote from the last E.U. election, when the party was a newcomer protesting Greek bailouts.

But recent polls show it hasn’t gained support since the 12.6 percent it won in Germany’s 2017 federal election, and may have even lost a bit.

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“These elections are part of the great shift in politics — they’re a move away from the old normal, but we aren’t there yet,” said Heather Grabbe, the director of the Open Society European Policy Institute. “What you see across Europe is people moving out of mainstream parties to alternative parties.”

Another X-factor for the far right will be fallout from Austria, where the government collapsed in spectacular fashion several days ago after a video revealed the leader of the country’s premier far-right party apparently willing to engage in corrupt deals with Russians.

The scandal doomed a coalition between the center right and the far right that some in both camps had touted as an alternative future for Europe beyond the cozy left-right coalitions that have dominated in Brussels.

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Britain’s participation in the election may provide a shot of sugar for Euroskeptics, with Nigel Farage’s Brexit Party set for a good showing on Thursday. But those lawmakers will leave the European Parliament whenever Britain finally manages to quit the bloc.

In France, President Emmanuel Macron has framed the election as a chance to move toward a more integrated Europe, but one that better responds to the insecurities that have fueled nationalist movements. He has campaigned aggressively and has effectively “declared the poll to be a referendum on his presidency,” the Eurasia Group political consultancy wrote in an analysis this week.

If he fails to best the Marine Le Pen-led far right, the analysis concluded, “the final three years of his presidency — and hopes of pushing through deep reforms of education, pensions and the civil service — will have been damaged.”

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Much may depend on whether he can convince French voters that he can shake up Europe, but in a way that is different from the radical visions of the far right.

“The more the mainstream is tempted to stay with the status quo,” said Möller, of the European Council on Foreign Relations, “the more it is that the parties on the fringes will succeed.”

Witte reported from Berlin. Quentin Ariès in Brussels contributed to this report.