EU leaders embrace multi-speed Europe amid tensions
France, Germany, Italy and Spain have backed the idea of a multi-speed EU, as the 28-nation bloc prepares to mark 60 years since its founding treaty.
"Unity does not mean uniformity," French President Francois Hollande said as he hosted the other leaders in the ornate Versailles Palace near Paris.
The EU Commission accepts that projects do not have to involve all EU members.
Brexit - a psychological and budgetary blow - now overshadows the anniversary, the BBC's Kevin Connolly reports.
EU leaders are focusing on a strategy of promising both deeper co-operation but also the possibility of different member states joining common projects at times that suit them, our correspondent says.
After Brexit what next?
In some respects the EU is already a multi-speed organisation. Not all members are in the Schengen border-free zone, and 19 of the 28 use the euro.
The UK, poised to trigger the withdrawal mechanism soon, already has many opt-outs from EU policies.
"Italy wants a more integrated EU, but one that can allow various levels of integration," Italian Prime Minister Paolo Gentiloni said.
EU summit talks in Brussels on Friday will focus on how the EU moves forward post-Brexit, amid tensions over integrating migrants, globalisation and how to revive ailing eurozone economies.
Versailles was a symbolic place to hold such talks - the palace where peace in Europe was mapped out after World War One.
German Chancellor Angela Merkel said "we need to have the courage for some countries to go ahead if not everyone wants to participate.
"A Europe of different speeds is necessary, otherwise we will probably get stuck. If Europe gets stuck and doesn't develop further, then this work of peace may run into danger faster than one might think," she said.
The 1957 Treaty of Rome established the goal of "ever closer union". And the 60th anniversary is an occasion to stress unity, amid widespread speculation that the EU could disintegrate.
Poland is among the newer EU member states which view multi-speed development with suspicion.
Since the end of communism they have been catching up economically. And as net recipients from the EU budget they fear being left behind by their stronger European partners.