With 10 new countries about to join the European Union, and Turkey banging ever harder on the door, the question of just how much further it can stretch its borders is forcing the bloc to ponder its very identity.
"We can't give people the impression that we will continue to expand and expand and expand," European Commission President Romano Prodi said recently. "Otherwise our citizens won't know which community they belong to."
Europeans must instead consider forming "a circle of friends" with countries around the EU who would not become members but who would enjoy privileged relations with the bloc.
"We'll share everything with them except our institutions," Prodi told the European Parliament. "I believe we must break with the reasoning that contrasts the countries on the inside with those on the outside."
Valery Giscard d'Estaing - a former French president who chairs the convention mapping out a strategic vision for the EU - set a cat among the pigeons last month when he said the idea of Turkish membership would be the "end of the European Union."
The comment led to fierce debate as to exactly how far the EU, which currently has 15 member states, could or should extend its borders.
"The border issue touches on the question of the very identity of the European project," says Jean-Michel de Waele of the Free University of Brussels.
Yves Meny, president of the European University Institute in Florence, Italy, says the EU needs to "offer a serious and attractive alternative to membership of the club."
"Today people have the impression that you're either in the club or you're not. If you're in the club there are a lot of advantages, but if you're outside then it's hell."
There are plenty of hopefuls in the "hell" of outside.
Aside from the 10 lucky states, mostly in Eastern Europe, set to get their formal invitation to join in 2004 at a showpiece EU summit next week in Copenhagen, there are Romania and Bulgaria who are likely to be let in by 2007.
Then there is of course Turkey, of which only "a very small part" actually lies inside Europe, as Giscard d'Estaing reminded any Europeans who might try to overlook this awkward geographical fact.
The predominantly Muslim eastern Mediterranean state's foreign policy is currently focused on getting a start date at the Dec. 12-13 Copenhagen summit for negotiations to join the largely Christian EU.
At the other end of the Mediterranean is the North African state of Morocco, another Muslim state, and one which has already had its membership request politely but firmly declined.
Israel is a further country which would like to join the European club but whose geography can hardly be used as an argument.
In the Balkans there are various states that once made up Yugoslavia whose bids have been welcomed. One of these, Slovenia, is one of the 10 states due to be invited in next week.
Further east, hopefuls include Ukraine and Moldavia, and even Russia and the Caucasus states of Azerbaijan, Georgia and Armenia have expressed interest.
The Cold War had imposed clear limits to the EU's expansion but these disappeared with the fall of the Berlin Wall in 1989.
"The frontiers of Europe are the frontiers of the European Union that together we seek to create," says Yves Meny.
Defining those frontiers means defining the politics that guide the EU, and that "is something which some people want to avoid at all costs," he says.
Certain "lukewarm Europeans" who are fond of the slogan "wider is wiser" favor expansion because "the more you dilute, the more Europe becomes nothing more than a vast free trade zone," says Meny.
But he adds that "it is not our vocation as the EU to absorb everything that can be called European" from either an economic or a geographic point of view.
"Nobody is brave enough to say Europe must have borders and should ensure that these borders are not walls but simply the delimitation of a common political space," he concludes.