Britain's parliament is buzzing with frenzied campaigning as MPs build support for rival plans to end the deadlock over Theresa May's Brexit deal.

In a statement on Monday, the prime minister dashed hopes that she would unveil a plan B that modifies a deal she forged with Brussels which parliament rejected last week. Critics have said it was a case of "plan A all over again".

May stuck to her script, doggedly signalling that she would not change course as the March 29 deadline for Britain to leave loomed – deal or no deal.

What did May say?

May's statement set out three "changes" to her Brexit strategy.

First, she threw an olive branch to parliament, promising to be more "flexible, open and inclusive".

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Second, she promised to embed protections on workers' rights and the environment in any deal – in a sop to the main opposition Labour Party.

Third, she pledged to win concessions that would overcome the main hurdle to her plans – the divisive "backstop" demanded by the EU to avoid creating a customs border between Northern Ireland and the Republic of Ireland.

In short, the prime minister offered nothing new – while restating her opposition to a second Brexit referendum and rubbishing talk of extending Article 50, the European Union mechanism setting the March deadline.

Many MPs believe extending Article 50 is the only way to avoid leaving without a deal – which economists warn would be disastrous.

What happens now?

In a cabinet meeting on Tuesday, Foreign Secretary Jeremy Hunt reportedly questioned May's approach, suggesting EU concessions on the backstop would not win over sceptical Conservatives.

Meanwhile, May's lukewarm efforts to consult opposition parties have floundered.

A formal vote on the strategy outlined in her statement will take place on January 29 – giving MPs a week in which to thrash out game-changing amendments to alter the Brexit outcome.

How many amendments are being tabled?

MPs have until Monday night to table amendments, making it too soon to say how many there will be.

These could be merged by the powerful Speaker of the Commons, John Bercow, who will select which go forward.

Diverse options are now taking shape and their champions are parading them in a parliamentary beauty contest before next week.

Who are the big hitters - and what chance do they have?

Some amendments are turning heads.

Labour leader Jeremy Corbyn was quick off the mark with a call to let MPs vote on different options to avoid a no-deal Brexit – including a second referendum.

The party is divided on this issue and the move marks a step towards accepting it – but is unlikely to win support from sympathetic Conservatives who say it does not get straight to the point.

A cross-party amendment designed to block a no-deal Brexit by the Labour chair of the home affairs select committee Yvette Cooper and former Conservative minister Nick Boles has raised eyebrows.

They want to extend Article 50 if there is no deal by the end of February - and seem to be gathering steam.

Pro-European Conservative Dominic Grieve, a former attorney general, is calling for parliament to wrestle control of the Brexit timetable from the government – enabling MPs to then do whatever they like.

Grieve has form and has already drawn blood against May.

The Labour chair of the Commons Brexit committee, Hilary Benn, is calling for "indicative" votes to gauge support among MPs on a suite of Brexit options – but there are fears this may not end the deadlock.

Labour MP Stella Creasy wants Brexit to be delayed for a "citizens' assembly" to determine what the country at large wants. This has some heavyweight backing – but takes parliament into uncharted waters.

Pro-Brexit MPs also want their say.

An amendment by Andrew Murrison, chair of the Northern Ireland affairs committee, to curtail the backstop in 2022 throws down the gauntlet to the EU – but Labour will never back it.

And there is a strong expectation that at least one MP will press the "nuclear" button – with a no-nonsense motion formally demanding a second referendum or "People's Vote".