Wednesday: Sir Oliver Letwin has indicated he will try to seize control of the Commons agenda again to pursue his soft Brexit plan.
Exasperation is rising across the country that is angrily split down the middle over staying a member of the European Union or quitting. If it does not a present a plan, the United Kingdom could fall out of the bloc without a deal.
If the government can't bridge the gap by April 12, Britain will crash out of the European Union without a plan for future relations, damaging its economy, undermining the country's unity and diminishing its stature in the world.
If Mrs May wants to hold another vote on the deal in Parliament, it has to comply with Commons Speaker John Bercow's ruling that it can only be brought back with "substantial" changes. The process will be the same as last week: MPs will mark "yes" or "no" alongside each option.
Parliament rejected all eight alternative options put to a vote last week. The results are not binding on the government.
British MPs will try again to chart a new Brexit path on Monday after rejecting Prime Minister Theresa May's deal for a third time, but the European Union warned its patience was wearing thin. In particular, it would remove the need for customs posts and border checks between Ireland and Northern Ireland.
This proposal is backed by Tory Remainer Nick Boles, Labour's Stephen Kinnock, and the left-wing Scottish National Party (SNP), It would mean the United Kingdom joining the European Free Trade Association (EFTA) and European Economic Area (EEA), meaning the United Kingdom would remain part of the EU's Single Market (where countries trade with each other each other without restrictions or tariffs), retaining freedom of movement of EU citizens without immigration checks or limits.
More than half of her Conservative lawmakers signed a letter Saturday insisting May decide to go for a no-deal Brexit and leave without any agreement with Brussels, a move that could wipe out 10 percent of Britain's trade, according to economists, disrupt crucial supply chains and push Britain into a recession.
A similar motion on March 27 was defeated by 400 votes to 160.
While some pro-European members of May's cabinet might support a customs union, she herself is opposed and it threatens mass rebellion among the rest of her ministers. To prevent this, May would probably have to call a vote on an election before that legislation was passed.
Last week it lost by only eight votes, with 264 in favour and 272 against.
Another option with significant support is for any Brexit deal to be put to public vote in a "confirmatory referendum". In truth, while May should carry responsibility for failing to get Parliament to gather round a consensus on Brexit, lawmakers have had plenty of opportunity to vote for Brexit via her plan. A two-thirds majority is required for the government to force a poll. If that fails, parliament should vote on "no deal".
But it has been roundly rejected by lawmakers on both sides of Britain's Brexit divide.
"In a post on twitter, Nicola Sturgeon said: "[It's] really important to remember that tonight's votes are not on a preferential basis - an SNP vote for [the single market and customs union] would only be to keep that option alive in case it later becomes only alternative to a harder Brexit.