Nationals of the western Balkans (bar Kosovars) can get short-stay visa waivers to enter Schengen.
Besides all this, even full members of Schengen do not always apply the rules.
The new Schengen proposals will be high on the agenda of EU government talks next month.
Any policy changes will have to be approved by parliament and the Schengen zone governments.
The Schengen zone covers 22 EU states and three non-EU countries - Iceland, Norway and Switzerland.
In 2010 Poland issued 7% of all Schengen visas, but as many as one-fifth of long-stay ones.
So, the French president has threatened to suspend participation in the Schengen agreement unless it is reformed.
The passport-free Schengen area, often criticised as opening the doors to migrants, now makes for smoother trips.
The UK and Irish Republic still maintain passport controls, but comply with some of the Schengen provisions.
While the Schengen visa system allows holders to visit multiple European countries, Britain requires a separate visa.
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Eight of them (Romania and Bulgaria are the exceptions) have already joined Europe's Schengen passportless travel zone.
And in areas such as Schengen, there can be little real objection to an advance guard plunging ahead.
France gave out 2.2m visas, the most of any Schengen country, but many had only limited territorial validity.
The European Commission is due to submit a report on the operation of the Schengen system in May.
Schengen countries apply common procedures on the EU's external borders and their police forces have a common database.
To a degree, multi-system Europe exists already, in the euro and in the Schengen rules on crossing frontiers.
And Britain has also opted out of the abolition of internal European frontier controls, negotiated through the Schengen agreement.
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In the next few weeks Bosnians and Albanians are expected to be granted visa-free travel to Europe's Schengen area.
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Austrian officials say Germany and Italy have shown understanding for the decision to temporarily withdraw from the Schengen agreement.
The two countries have sought Schengen entry since joining the EU in 2007.
Schengen will be discussed by EU home affairs and justice ministers on Thursday.
Britain has not adopted the euro and does not participate in the Schengen system of free movement of people.
Yet, for all these problems, few governments would welcome the scrapping of Schengen.
Applicants to enter Schengen must provide a ream of documents, including proof of health insurance, travel tickets and hotel reservations.
But the row could hinder its attempt to be granted visa-free travel within the Schengen area of 25 European countries.
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Yet, given today's fears in western Europe over legal and illegal migration, the expansion of Schengen is some way off.
In late October champagne was on offer at Milan and Rome airports to mark the country's full membership of Schengen.
Sanctions could include cutting funds, extending the monitoring of the judicial system or blocking membership of the Schengen passport-free zone.
Since 19 December 2009, its citizens have not needed visas to visit most EU countries - those in the Schengen zone.
The European Commission allowed temporary re-introduction of border controls, in breach of the Schengen convention of the free movement of people.
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