Despite the breakdown of talks last week, the government could resume discussions with Labour on a compromise Brexit deal today.
After failing to get the DUP and enough Tory MPs to support her EU withdrawal agreement, Theresa May is hoping she can win Labour backing through the cross-party talks.
With seemingly little progress so far, the prime minister might eventually have to ditch her opposition to a post-Brexit customs union with the EU, which Labour is demanding.
This would anger a large number of Conservative MPs, but might allow Mrs May to finally get a deal through the House of Commons.
In the House of Lords, peers will conclude their scrutiny of a bill from Labour’s Yvette Cooper and Tory ex-minister Sir Oliver Letwin.
If passed, this would force the prime minister to consult the House of Commons on the length of any further delay to Brexit she requests from the EU.
Mrs May will head to Berlin and Paris for talks with German chancellor Angela Merkel and French president Emmanuel Macron, just a day before an emergency EU summit.
In Westminster, if Ms Cooper and Sir Oliver’s bill is passed into law, the prime minister will have to table a motion in the House of Commons promising to request another extension to the Article 50 negotiating period.
This motion could be amended by MPs to either shorten or lengthen – or add further conditions to – any Brexit delay.
If the government does strike a deal with Labour, Tuesday could even see another “meaningful vote” on the prime minister’s withdrawal agreement.
Should her talks with Labour not be successful, the prime minister has promised to hold votes on various Brexit alternatives among MPs – although this week could be too soon for the House of Commons to stage such votes.
Two previous rounds of so-called indicative votes in the House of Commons have seen MPs reject any alternative Brexit plan.