The divided European Union's 28 national leaders were to spend a third consecutive day on Tuesday arm-wrestling over who should hold the bloc's most prominent jobs until nearly 2025.
Some leaders dozed off from exhaustion during talks overnight into Monday that ended with Italy and ex-communist eastern states blocking socialist Dutchman Frans Timmermans from running the EU's executive Commission.
In the ever more fragmented bloc, leaders are trying to balance political affiliations, varying interests of different regions, and an acute gender gap in senior echelons.
It is highly unusual for a summit to run into a third day, and this round is already the third attempt to decide the jobs.
The inability to reach consensus bolsters criticism from anti-establishment nationalists and undermines the EU's image as it faces multiple external challenges including from the United States, Russia, Iran and China.
Apart from the Commission, which monitors states' budgets and proposes new laws, other top jobs up for grabs later this year include the presidents of the European Parliament and the European Central Bank, as well as the top diplomat in Brussels.
The fifth position is the head of the European Council, currently held by former Polish premier Donald Tusk, who is tasked with building compromises among members.
EU leaders must seal a deal on Tuesday or risk being overtaken by the new European Parliament, which holds an inaugural session on Wednesday after a continent-wide election in May. It is due to pick its new president and could act independently barring agreement of the 28 national capitals.
The new EU assembly must then also back any candidate to head the Commission nominated by national leaders.
While Timmermans had enough support to succeed under EU rules, opposition from Italy, Hungary, Poland, the Czech Republic and Slovakia risked poisoning future decision-making.
The eastern nationalist governments have a grudge against him for leading criticism of them for curbing the independence of judges, media, academics and non-governmental groups.
Italy faces imminent action from the Commission - where Timmermans is a deputy head - over its high debt.