EU leaders are in Brussels to consider candidates for the organisation's most important jobs in the wake of parliamentary elections.
The presidency of the EU Commission, currently held by Jean-Claude Juncker, is among those up for grabs.
One of the candidates, Frans Timmermans, compared the process to brutal TV drama Game of Thrones.
The elections saw the big centrist blocs lose their majority with nationalists and Greens gaining ground.
It leaves the EU more fragmented, so finding consensus may be harder than in the past.
The talks over dinner on Tuesday may not even result in a shortlist of candidates and the haggling is likely to take months.
It is more an occasion for leaders to assess the political mood and explore possible combinations, to ensure a stable balance of political opinions, geography and gender.
UK Prime Minister Theresa May will participate, but Brussels sources say there will be little or no discussion of Brexit.
The other top EU officials to be replaced later this year are: European Council President Donald Tusk (Polish); European Central Bank President Mario Draghi (Italian) and EU High Representative for Foreign Affairs Federica Mogherini (Italian).
After lengthy negotiations, the new top officials will take up their posts on 1 November, except for the new European Council chief, who starts on 1 December.
In 2014 Mr Juncker was chosen to head the Commission as the centre-right European People's Party (EPP) candidate, after the EPP had won the election.
But it is a much tougher challenge this time for the EPP's candidate Manfred Weber - a German - after his bloc shrank from 217 seats to 180 in the 751-seat parliament.
Party leaders from the EPP and other parliamentary groupings have met in Brussels in an effort to agree on a "Spitzenkandidat" - lead candidate - for Mr Juncker's job. The Commission enforces EU rules and drafts EU laws, so it is the most coveted post in the 28-nation bloc.
There are already signs of disagreement among two of the EU's major figures, German Chancellor Angela Merkel and French President Emmanuel Macron.
She backs Mr Weber for the presidency of the Commission, but he suggested other names including chief Brexit negotiator, Michel Barnier, liberal candidate Margrethe Vestager and Mr Timmermans, a centre-left candidate from the Netherlands.