Theresa May is due to open the debate on amendments to her Brexit plan, which could shape future talks with the EU.
Conservative MPs have been told to back a proposal for an alternative to the Irish backstop – the « insurance policy » against the return of a visible border.
International Trade Secretary Liam Fox told the BBC this would give the PM a « strong mandate » to return to Brussels to negotiate changes to the backstop.
It is not yet known which amendments will be chosen for a vote.
BBC political editor Laura Kuenssberg said that, for the government, Tuesday was about turning « a thick wall of resistance » into a hurdle that « at some point they might overcome ».
Speaker John Bercow will say which amendments are going to be put forward at the start of the debate at about 13:45 GMT, with Mrs May now set to open the debate – with voting taking place in the Commons from 19:00 GMT.
MPs have been tabling proposed changes to the government’s plans to try to influence the direction of Brexit since Mrs May lost the vote on her original deal earlier this month.
They include proposals to rule out leaving the EU with no deal or to delay Brexit from its scheduled date of 29 March.
The prime minister’s official spokesman said Tuesday’s voting would be followed « as soon as possible » by a second meaningful vote on whatever deal has been secured with Brussels.
But BBC political correspondent Iain Watson said Tory MPs on both sides of the argument are starting to draw up more alternatives, in case no progress can be made and the UK leaves the EU without a deal.
Former Remainers, including ex-Education Secretary Nicky Morgan and government ministers Stephen Hammond and Rob Buckland, have been working with Brexiteers Jacob Rees-Mogg and Steve Baker on the plan – in talks co-ordinated by Conservative MP Kit Malthouse.
According to a leaked document, the proposal drawn up by the rival factions would extend the transition period – during which the UK would continue to follow EU rules and pay into its budget – from the end of 2020 to December 2021, to allow more time to reach a free trade deal.
EU citizens rights would be guaranteed during this time, there would be no customs checks on the Irish border and the UK would pay the £39bn so-called « divorce deal ».
The Democratic Unionist Party (DUP) – which props up Mrs May’s government – has endorsed the « Malthouse » proposals.
DUP leader Arlene Foster said the plan could « unify a number of strands in the Brexit debate » and was a « feasible alternative to the backstop proposed by the European Union ».
But the EU was « standing tough » on its position of no renegotiation and they were « mesmerised » with what was happening in Parliament, BBC Europe editor Katya Adler said.
Will MPs find agreement in their plans?
« It might not be 326 that matters ».
According to one cabinet minister, that’s the strange situation that Brexit has led us to.
The government’s ambition is so low – or its hurdles so high – that what No 10 seeks to do on Tuesday is not to win (326 is a majority in the House of Commons), but to reduce the scale of resistance to their central policy that, in the words of another cabinet minister, only the « hardliners oppose », so that Theresa May can get the rebels down to a « few dozen », so then they can crack on.
- Read more from Laura
Mrs May took the deal she had negotiated over the past 18 months with the EU to Parliament on 15 January for a « meaningful vote » – having delayed it from December – but MPs rejected it by a record-breaking 432 votes to 202.
She addressed a meeting of her backbench MPs on Monday night and numerous sources said she would be backing what is known as the « Brady amendment » – a measure put forward by Sir Graham Brady, the chairman of the backbench 1922 committee of Conservative MPs.
Sir Graham wants to see the Irish backstop replaced by what he calls « alternative arrangements to avoid a hard border », but would otherwise support the prime minister’s deal.
Mr Fox told BBC Radio 4’s Today programme: « I think we should send the prime minister back to Brussels with a strong mandate to be able to say if you compromise with us on this one issue, on the backstop, we would be able to a get an agreement – an agreement that is almost there. »
He said if the Brady amendment was passed later, negotiations would have to be reopened « if that’s what’s required to get agreement on the backstop », adding: « No negotiation is over until it’s over. »
Mr Fox told BBC Breakfast the worst-case scenario would be no Brexit.
He said: « We have to ensure that Brexit itself is safe and we know that there are those in the House of Commons who would happily see us not leave the European Union at all. »
Senior EU representatives have repeatedly ruled out reopening negotiations with the UK over Brexit, and have insisted the backstop – the insurance policy against a return of a hard border between Ireland and Northern Ireland – must be included in any deal.
And Ireland’s European Affairs Minister, Helen McEntee, said: « There can be no change to the backstop. It was negotiated over 18 months with the UK and by the UK. »
The European Research Group, led by Eurosceptic Mr Rees-Mogg, had initally said the group would not back the amendment.
But Mr Rees-Mogg told the BBC on Tuesday that if the Brady amendment had government support and if it meant reopening the withdrawal agreement – the part of Mrs May’s deal that lays out how the UK will leave the EU – it would be « very different » from a backbench plan.
« Let’s see what the prime minister says at the despatch box today and what the Brady amendment really means, » he said.
Former foreign secretary and prominent Brexiteer Boris Johnson tweeted that he would back the Brady amendment if Mrs May indicates that she will press Brussels to reopen the withdrawal agreement.
« We need to go back into the text of the treaty and solve the problem, » he said.
« That is the way to unite Remainers and Leavers in the Conservative party and across the country. »
Will Brussels budge on the Irish backstop?
By Katya Adler, Europe editor
Boris Johnson insists on them, Graham Brady is pushing hard for them, Prime Minister Theresa May seems to be praying for them and Dublin is deeply worried at the thought of them – but will the EU ever actually « give in » and make changes to the backstop?
It’s a tough one.
The EU certainly never intended to budge on the backstop – painfully negotiated with the UK over 18 months and signed off last November by Mrs May and her cabinet.
But Europe’s leaders didn’t imagine the UK would still be in such flux over Brexit so very close to B-day on 29 March.
- Read more from Katya
Mrs May has also faced calls from Labour, and a number of other MPs, to rule out the scenario in which the UK leaves the EU without a deal.
A number of Remain-backing MPs are supporting an amendment by Labour MP Yvette Cooper that would create a bill enabling Article 50 – the mechanism by which the UK leaves the EU – to be delayed by up to nine months if the government does not have a plan agreed in Parliament by the end of February.
Shadow Northern Ireland secretary Tony Lloyd told BBC Radio 4’s Today programme that Labour’s priority was to ensure that a no-deal scenario was not possible, « that Theresa May cannot be under any sense of ambiguity that she can use the tactic of saying ‘It is my deal or no deal’. No-deal must disappear. »
Former Prime Minister Tony Blair has urged Labour MPs to back the plans, saying it was « sensible » to « take this time and reach clarity ».
The debate will be the first in which MPs on parental leave will be able to nominate another MP to vote on their behalf after the Commons unanimously chose to implement a year-long trial of proxy voting. Labour’s Tulip Siddiq, who delayed giving birth to attend the Brexit-deal vote on 15 January, is set to be the first person to benefit from the move.
Meanwhile, the government has announced its plans for EU citizens coming to the UK in the case of a no-deal Brexit, saying it would « seek to end free movement as soon as possible ».
The Home Office said that for a « transitional period » after Brexit – set for 29 March – EU citizens will be able to enter the UK to visit, work or study as they do now, but after three months they would need to apply for « European Temporary Leave to Remain », which would last three years.
Home Secretary Sajid Javid said it was a « practical approach » and would « minimise disruption to ensure the UK stays open for business ».