The centrepiece is a plan to take any refugees and migrants who cross the sea to Greece in smugglers' boats and return them, directly, to Turkey.
European Union officials say whatever is finally agreed "will comply with both European and international law". Privately, though, some admit that, while the assessment of their lawyers is "quite promising", there are legal hurdles that must be overcome.
So can Europe carry out mass returns of entire groups of people? UN officials have cited the European Convention on Human Rights, arguing that it explicitly prohibits the collective expulsion of foreigners. And they say that under international law, it is not illegal for someone fleeing persecution and conflict to cross a border and ask for asylum.
Around 90% of those arriving in the Greek islands say they are fleeing conflict, primarily from Syria, Iraq or Afghanistan. Under international law, each person's case must be heard on an individual basis, not as a group, because they may have very good reasons for seeking protection.
The second difficulty, UN officials have said, is that while returns can be legal, people can only be sent back to a country that is safe, is able to care for them, give them full access to work, to education, to healthcare, and, most important of all, will take responsibility for processing the individual's asylum claim.
The reason many Syrians are leaving Turkey is that it can't provide work, education and healthcare for them all. A system to apply for asylum in Europe from Turkey doesn't exist yet.
Until now, the EU has not returned people to Turkey. It hasn't viewed Turkey as what's called a "safe third country". Turkey is not a full member of the Geneva Convention. It does not offer Syrians asylum, only a lesser form of international protection. And other groups like Iraqis and Afghans don't even have that option in Turkey. So while returning Syrians is questionable, returning non-Syrians may be even more problematic.
Even if all the legal issues are settled there remains the practical problem of how Greece would send back all those making the crossings. Desperate people, men, women and children would have to be rounded up, held and then transported back across the sea.
In exchange for the mass returns, the EU is offering to take in large numbers of asylum seekers directly from Turkey. So for every Syrian sent back to Turkey, one already in Turkey will be resettled in Europe. But finding EU countries willing to accept the new arrivals may not be easy.
Last year, EU countries pledged to shift thousands of refugees directly from Greece, Italy, and Turkey and give them new homes in the EU. Just a few hundred have actually been moved. Could countries achieve now what they have failed to make happen so far?
Hungary has made clear that it is not prepared to accept quotas under this new plan. Other countries in central and eastern Europe are also opposed. So to make this work, a "coalition of the willing" - countries prepared to welcome Syrians - will have to be assembled. Germany and the Netherlands may have to be the leaders here, but they will need support from other states too.
Among Turkey's demands to secure a deal is visa-free access to the EU for Turks, ideally by the end of June, but there is significant political resistance. It would allow more than 70 million Turks to travel (but not work) visa-free in Europe's Schengen zone.
That hasn't happened before now because some EU countries have worried about the political backlash at home from anti-immigrant parties. France in particular has been opposed. The indications from behind closed doors at the summit were that President Francois Hollande may be willing to accept a deal on visas.
But then there is the problem that Turkey does not officially recognise the Greek-Cypriot government in Nicosia (Cyprus is an EU member). That's one issue to overcome, and there is also significant opposition to visa concessions for Turkey in the European Parliament, which would have to approve the change as well.
Even if all of these issues are resolved, sources say that EU countries will probably still insist Turkey meet all the technical conditions necessary for visa-free access. The hurdles, such as Turkey introducing more sophisticated biometric passports, are significant.
This is another of Turkey's demands. It may be largely symbolic, as most EU countries believe Turkey is years away from achieving EU membership, but making any headway on this will be even harder than on the subject of visas.
Opposition from Cyprus is one big issue here. Turkey must recognise the government in Cyprus before any new discussions open. Cyprus has stated clearly that it has a clear understanding from other EU countries that "Turkey cannot use its role in the refugee crisis... to ask for exchanges as regards its EU accession course".
Other countries like Italy and Belgium have doubts about making concessions at a time when there are serious concerns about Turkey's political direction, about declining media freedoms, and worries about a shift towards greater authoritarianism in Turkey's politics.
Privately, EU sources say agreement even to open any new accession discussions will be "very difficult" and is one of the most important things to clarify if a deal is to be done next week.
For all the difficulties, though, there are powerful, political reasons why all sides want a deal. The EU as a whole wants to regain control of events in this refugee crisis. There is a real concern that countries have started going it alone, consensus has broken down, and the EU has to find a plan that reverses that dynamic.
There is also a fear that if the refugee crisis remains unresolved, it could affect Britain's EU referendum. Angela Merkel needs a deal as she's come under huge political pressure at home. And the crisis has caused a real rift between the leaders of Germany and Austria that needs to be mended.
Other EU leaders want to show their electorates they can protect the EU's borders, fearing that otherwise anti-immigrant parties will seize the political initiative. Closing some border crossings to deal with the refugee crisis has had economic costs too.
And a deal suits Turkey as well. It is hosting millions of refugees and is under serious pressure because of the way the war in Syria has shifted with Russia's involvement. Despite their difficulties, the EU and Turkey both benefit if they can make a strategic relationship work, and they need support from each other to deal with the crises they are facing.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.
European leaders are billing their new proposal to deal with the refugee and migrant influx as a "game-changer", but the scheme is not agreed yet and there are doubts about whether it it is practical or even legal.