Why is Theresa May on an EU diplomatic charm offensive?

After MPs passed the Brady amendment last week calling for the Irish backstop to be replaced with “alternative arrangements”, the prime minister pledged to renegotiate with Brussels in an effort to secure the changes she said parliament had demanded.

Since then, officials and ministers have been working up potential proposals in three areas in particular: an exit mechanism; an end date; and the technology-based alternatives favoured by many Brexiters.

The prime minister will travel to Brussels on Thursday to meet Jean-Claude Juncker, the European commission president, for the first time since her deal was rejected and test the appetite for the kind of legally binding change she says she needs to secure a majority.

Does she have a specific proposal?

Not yet. Downing Street says officials are working urgently on all three proposals. Daily meetings are being held with the Tory MPs behind the so-called Malthouse compromise, which focuses on technological solutions.

The attorney general, Geoffrey Cox, has been working on the other two approaches: an exit clause or a time limit.

When Theresa May flies into town on Thursday insisting all three options are still in play, EU officials could be forgiven for thinking the Irish prime minister, Leo Varadkar, was right when he said the phrase “alternative arrangements” “can mean whatever you want them to mean”.

She may want to test the potential support for different options, despite senior figures repeatedly insisting the 585-page withdrawal agreement cannot be renegotiated.

Is it all about the backstop?

No. The government is also working on ways of winning over another group of potential supporters for a tweaked version of May’s deal: Labour MPs.

Several Labour MPs have made clear they could not support another referendum and might consider backing a deal, if the government could offer stronger reassurances on workers’ rights and environmental standards.

May and her ministers have met union leaders and MPs in recent days and are drawing up proposals they hope will win over Labour backers already sceptical about a referendum.

However, Downing Street believes these are changes that can be achieved through domestic legislation, without having to revisit the Brexit deal.

Will there be another ‘meaningful vote’ next week?

It doesn’t look like it. No 10 has said the prime minister will bring back a revised withdrawal agreement for approval by MPs “as soon as possible” but the cabinet has been warned that it is unlikely to be in the next few days.

If there is no deal to bring back for approval, the prime minister has promised to table a motion in parliament on 13 February, which MPs could then amend.

That was a demand of senior Conservatives, including from within cabinet, who were anxious to avoid no deal, and were threatening to back the Cooper-Boles amendment which would have empowered MPs to decide the next steps, including requesting an extension to article 50.

Another such amendment could be voted on next week, or MPs may decide to give the prime minister time to play out her negotiating strategy in Brussels first. Certainly, supporters of a second referendum are again expected to stay their hand.

What if she fails to win the support of parliament in another meaningful vote?

May’s deal was rejected by an overwhelming majority of 230 last month. She then managed to clinch a narrow victory in the vote on the Brady amendment, but with the more hard-nosed members of the pro-Brexit European Research Group (ERG) saying even changes to the backstop might not be enough to win them over, there is no guarantee she could scrape a deal through parliament even if Brussels caves in.

If a second attempt failed, she could still come back again, though it would surely be clear by that point that backstop tweaks would not be sufficient to get her over the line.

Could the Labour leadership support the prime minister?

It still looks a stretch, but not completely impossible. However, the prime minister would have to abandon her red line on a customs union, something she has so far proved doggedly unwilling to do, even in the face of that historic parliamentary defeat in January.

Will article 50 have to be extended?

It looks highly likely, as the shadow foreign secretary, Emily Thornberry, said in parliament on Wednesday.

But May has warned her cabinet not to speculate publicly about it. Downing Street points out that the EU27 would have to agree to an extension unanimously, and would be unlikely to do so just to allow squabbling MPs more time to coalesce around a proposal.

Could we end up leaving with no deal?

It’s still not likely, and several cabinet ministers, including the business secretary, Greg Clark, hinted heavily on Wednesday that they would rather resign than support it as an aim of government policy.

But as the prime minister has repeatedly said, the only sure way for parliament to prevent no deal is to agree to a deal. And that still looks some way off.