London, England - A series of key votes on Tuesday could begin charting a way out of Britain's Brexit impasse as the clock ticks towards March 29, when the country is due to quit the European Union.

MPs will test their own proposals to resolve the stalemate caused by a resounding rejection of Prime Minister Theresa May's exit deal with the EU.

Their plans could set a new direction for the country, or they could underline the debilitating lack of consensus that persists on the most divisive issue the country has faced for generations.

What's happening and why it's important

Tuesday will mark the first time MPs have been given the chance to propose their own solutions to the deadlock and comes after they rejected May's draft EU agreement earlier this month.

The Conservative prime minister was expected to put forward a Plan B, but has stuck doggedly to her guns, trying to build support for a revised version of her original blueprint.

MPs will vote on amendments to her approach selected by the powerful Speaker of the Commons John Bercow; 19 had been submitted by Monday and he may choose four.

What's expected

Three proposals have gained a head of steam among MPs.

Sir Graham Brady, the influential head of the Conservative Party's 1922 Committee, wants to overcome the main hurdle to May's deal by replacing the "Irish backstop".

Conservative MPs hate this mechanism, which would prevent a customs border between Northern Ireland and the Republic of Ireland if the United Kingdom cannot agree on a future trade deal with the EU.

There needs to be considerable clarity coming from the UK in order for the EU to consider making changes. I am sceptical. Simon Bulmer, professor of European Politics at the University of Sheffield

Brady says his amendment would give May "enormous firepower" to demand concessions from Brussels and could simply be appended to her withdrawal agreement.

David Phinnemore, professor of European Politics at Queen's University Belfast, said: "If it does go through, then clearly, it is being seen by some MPs as a way of getting support for May's withdrawal agreement, and it also gives the prime minister a sense of what she needs to get from the EU.

"But whether the EU will be happy to pursue discussions on something appended to the withdrawal agreement is impossible to say."

A second amendment turning heads has been put forward by the Labour chair of the Home Affairs Select Committee, Yvette Cooper.

This seeks to prevent a "no-deal" Brexit, something economists warn would be disastrous, by directing the government to extend the deadline if there is no agreement by February 26.

Maddy Thimont Jack, a researcher at the Institute for Government in London, said: "The Brady amendment is obviously trying to express a view that the House will approve the deal as long as the prime minister negotiates or is able to address concerns about the backstop, whereas the Cooper amendment is really about MPs trying to take control of the process or timeframe."

A third amendment gaining cross-party support, drafted by Conservative Caroline Spelman and Labour's Jack Dromey, would simply block Britain from leaving the EU without a deal.

What influence do the amendments have?

Tuesday's votes could make all the difference, or none at all.

The EU insists the backstop can only be abandoned if the UK stays in a customs union with the bloc.

May's "red lines" - the negotiating points on which she refuses to budge - include a desire to control immigration from the EU, which means the UK cannot remain in its customs union and single market.

The Brady amendment rests on Conservative hopes that a clear statement of intent by MPs will prompt the EU to compromise, but there is no sign it will.

At the weekend, Ireland's foreign minister, Simon Coveney, stated baldly the backstop simply "isn't going to change".

Phinnemore said the Brady plan is in keeping with two years of British discussions that have failed to recognise the European position.

He said: "The EU line seems to be very strong on this: there are very few ways of getting around controls on the movement of goods on the island of Ireland without a customs union and without the regulatory alignment."

What will Europe do?

Whether MPs vote for May to renegotiate the backstop or even delay Brexit, this does not solve the UK's fundamental problem: the lack of a clear consensus.

Phinnemore said there are indications from the EU that if the UK signals its intention to relax its red lines, Brussels will talk.

"They would probably have to shift towards a permanent customs union arrangement for the UK as a whole. It is very difficult to see the EU moving away from the requirements for a backstop."

Simon Bulmer, professor of European Politics at the University of Sheffield, says that above all, Brussels is seeking clarity from what it sees as disarray on the British side.

"Europe is only going to make concessions if it is presented with a clear option and we have got to see whether that emerges in the voting.

"The difficulty is the noise of other proposals that may or may not be successful. There needs to be considerable clarity coming from the UK in order for the EU to consider making changes. I am sceptical."

Where does this leave Brexit?

There is no guarantee any of the frontrunner amendments will pass.

Pro-Brexit Conservatives are cooling on Brady's plan, and Labour MPs in constituencies that voted to leave the EU do not trust Cooper's.

Moreover, Cooper's amendment would not identify a consensus among MPs to halt a no-deal Brexit.

Bulmer believes an amendment tabled by the Labour chair of the Commons Brexit committee, Hilary Benn, calling for "indicative" votes to gauge support among MPs on a suite of Brexit options, may be a way forward.

"If there was a systematic review of the options to try and smoke out what is feasible as the way forward then the EU would take a more constructive way of looking at things.

"They have been around the houses on this so many times."