What is 'multi-speed'?
The idea of a multi-speed Europe is that some member states may choose to go faster, or slower, with European integration than others on certain policies.
In this scenario, countries wanting to move ahead on issues such as economic growth, border protection and defence could form smaller groupings, while countries not wishing to engage in these issues could participate to a lesser degree.
European Commission President Jean-Claude Juncker made this one of five possible scenarios for the future of the EU in a white paper earlier this month.
Germany and France have supported the idea, while certain Eastern and Central European countries have opposed it.
What exists already?
Ironically, today's EU is already a multi-speed Europe.
Some of its most far-reaching policies are limited to certain countries, notably the euro single currency, which has only been adopted by 19 out of the EU’s 28 member states. Similarly, only 22 countries are members of the visa-free Schengen zone.
Moreover, according to EU rules, groups of at least nine member states can embark together on policies in a process called "enhanced cooperation", without the other members’ involvement.
The EU holds a long tradition of deciding everything by unanimity. However this principle worked better when the bloc only counted a dozen members, rather than the current 28.
As it stands, proposals seen as urgent by a majority of member states can easily be vetoed by one.
A multi-speed Europe is seen as a solution to the deadlock. Tighter groups of member states could deepen ties, with more independent-minded states opting out.
Backers of such 'multi-speed' policies believe this is the way that seemingly impossible goals such as harmonised tax policies or an EU army could finally see the light of day.
Where does France stand?
At a mini-summit in Versailles on Monday, French President François Hollande said that “unity does not equal uniformity.”
"For this reason, I support new forms of cooperation," he said at a joint press conference.
He expressed the view that some countries can advance more rapidly than others, and can “go further in areas such as defence and the euro zone”.
German Chancellor Angela Merkel, who attended the mini-summit, agreed with Hollande. “A Europe of different speeds is necessary, otherwise we will probably get stuck.”
Who is against?
Poland's prime minister rejected the idea this Friday, a day after Warsaw fought with the bloc over the re-election of EU president Donald Tusk.
"We disagree with any talk of a multi-speed Europe," Beata Szydlo said.
Some Eastern and Central European countries are also opposed, as they fear being excluded from decision-making processes.