Theresa May meets the leaders of the remaining EU 27 today to press for a further extension to the Article 50 withdrawal process to June 30 to allow her more time to get a deal through the UK's Parliament.
German Chancellor Angela Merkel has suggested they “may well” go for a longer delay, although the UK would be allowed to leave “very quickly” if Parliament approves a withdrawal deal.
Political Correspondent Fiachra Ó Cionnaith outlines the key issues to be discussed at the latest special EU summit in Brussels tonight.
Q: EU leaders are meeting British Prime Minister Theresa May in Brussels this evening to discuss Brexit again. Why?
A: Anyone taking a passing interest in the Brexit crisis would be forgiven for thinking it is fast becoming a real-life version of Bill Murray's 1990s box office hit Groundhog Day - where the same day is repeated over and over again with no end in sight.
However, while the political choreography may be similar, each meeting of EU leaders in Brussels brings with it subtle changes that are taking us one step closer to a long-awaited conclusion to the crisis.
After Westminster ruled out the existing Brexit deal for a third time and all other alternatives in a series of votes at the start of this month, British prime minister Theresa May announced last week she is seeking another extension of the Brexit deadline from this Friday until June 30.
The June 30 extension request - which follows hot on the heels of the original March 29 to April 12 extension - is likely to be rejected by EU leaders this evening. They have made it clear it can only happen if Britain agrees to contest the MEP elections next month.
In a bid to avoid a crash-out Brexit in just 48 hours time, European Council president Donald Tusk has suggested an alternative option - an extension that would allow Britain to leave at any point within the next 12 months if MPs agree a workable way forward for both sides.
This second option is likely to be pushed on Ms May this evening at a meeting during which Mr Tusk stressed the British prime minister must not feel as though she is being "humiliated".
However, while a popular way out of the latest Brexit mess, several influential EU leaders - including French president Emmanuel Macron - are likely to insist the offer is on condition Britain agrees to contest the MEP elections and crucially not to deliberately trip up EU work over the next year.
If this is not agreed, rumours are circulating of a new June 1 no-deal Brexit cliff edge.
Q: What is likely to happen with the first option: a no deal crash out Brexit this Friday?
A: While this is still technically possible, a situation alluded to by Taoiseach Leo Varadkar during the Dáil's leaders questions debate on Tuesday, it is becoming increasingly unlikely - mainly because of the sheer damage it would cause all sides.
All indications from Dublin, London and Brussels are that the Friday, April 12, deadline will be replaced by one of the other options by this evening, notwithstanding a diplomatic disaster tonight.
Q: What is likely to happen with the second option: Ms May's June 30 extension request?
A: Just like last month, Theresa May has again put forward a late June extension request as the delay she believes is best suited to resolving the Brexit impasse.
Such a delay would be just about palatable to hardline Brexiteers who want to leave the EU quickly but understand a coherent plan still needs to be agreed before this can happen.
In addition, it would give Ms May and Labour leader Jeremy Corbyn breathing space to find a way to compromise on key issues, potentially leading to an eventual customs union-style Brexit.
However, the EU has made it abundantly clear - both last month and again in recent days - that a June 30 extension would cause havoc to the MEP elections and is highly unlikely to be accepted by member states.
Q: What is likely to happen with the third option: Donald Tusk's on year "flex-tension" proposal?
A: This is the option being pushed by the majority - but not all - EU member states.
In his traditional open letter before the EU summit, sent on Tuesday night, European Council president Donald Tusk said he is open to offering a potential year-long Brexit delay that would give Britain time to work out what it wants to do.
Under the proposal, Mr Tusk said Ms May could be told Britain can leave at any time within the next year provided she adheres to two conditions.
The first is obvious: running candidates in next month's MEP elections, with the EU saying this is essential to being given any long delay.
The second is more questionable, with French president Emmanuel Macron among a number of leaders who want any year-long "flex-tension" offer to only be made if Britain is effectively put in the EU back seat for a year and for regular reviews to ensure this is happening.
While the French view is a logical way to prevent Brexiteers from deliberately sabotaging EU work for the next 12 months, it may be difficult to impose as a member state has automatic rights to participate in EU budget talks and other matters.
Q: What is likely to happen with the fourth option: a potential new June 1 crash out date if nothing can be agreed?
A: If the June 30 and "flex-tension" options are rejected, it has been rumoured by high-level sources that the EU could propose June 1 as a new no-deal crash out Brexit deadline.
This previously unstated date, which comes just one week after the MEP elections, would give Britain and the EU enough time to finalise their no deal plans, but is seen as a last resort option, for now.
Q: EU leaders keep saying member states are united on the issue. Are they?
A: Publicly yes. Privately... we'll see.
Ever since last month's EU summit saw a flurry of competing Brexit extension dates proposed, there has been a sneaking suspicion EU leaders are no longer speaking entirely from the same hymn sheet.
This has been underpinned by well-placed Paris sources suggesting to media outlets that Mr Macron is running out of patience and is fine with Britain leaving as soon as possible.
However, on the surface at least, EU leaders insist they are continuing to speak with one voice on Brexit, albeit one voice that is beginning to speak out of different sides of the same mouth.
Q: The EU says it is being reasonable, while hard-line Brexiteers say the EU has blinked. Who's winning the Brexit wars?
A: This is a legitimate question.
The EU holds all the cards in that it can decide not to accept any more delays and simply hold Britain to its previous commitments, and can claim to have been reasonable in offering extensions.
However, after allowing one "absolutely final" extension last month, it has now opened the door for the trick to be repeated ad nauseum.
This might be good news for diplomacy, and there is nothing wrong with being the reasonable party in a row - particularly a row that has the potential to damage your own interests.
However, the emergence of extensions on the Brexit radar has watered down the previous threat of a cliff edge no deal Brexit date, something that unless it is handled carefully may encourage Brexiteers to push for more of what they see as concessions in the weeks to come.