EU leaders conducted a furious round of meetings Tuesday (July 2) in Brussels.
They're still deadlocked over who should get the bloc's top jobs.
On Tuesday Christine Lagarde emerged as a strong possibility for President of the European Central Bank.
She's currently chief of the International Monetary Fund.
Her name was put forward by French leader Emmanuel Macron.
He's also nominated German defense minister Ursula Von der Leyen to head the European Commission.
The proposals come after marathon talks got nowhere.
German Chancellor Angela Merkel has called on all sides to compromise.
A spokesman said she was "very positive" about Lagarde.
Other jobs including head of the European Parliament and the bloc's top diplomat are also at stake.
The appointments have to satisfy all EU member states and the big political parties.
Like many EU deals, that may mean the talks go on way into the night, or subsequent days.