Theresa May has said she will talk to the EU later about reopening the withdrawal agreement.
The EU has ruled out making changes to the legal text agreed with the UK prime minister.
But Mrs May has told her cabinet she will seek to do that, as MPs debate her plan ahead of a series of votes.
Conservative rebels who voted down her deal earlier this month are demanding legally binding changes to the controversial Irish backstop clause.
Conservative MPs have been told to vote for an alternative to the backstop, proposed by senior backbencher Graham Brady, but it is not yet known which amendments will be chosen for a vote.
Cabinet minister Liam Fox has said the “Brady” amendment it would give the PM a “strong mandate” to return to Brussels.
Some Tory Brexiteers have signalled they will now back Mrs May, despite previously threatening to rebel.
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 voting taking place in the Commons from 19:00 GMT.
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”.
Separately, Conservative MPs on both sides of the Brexit argument have been planning for a no-deal scenario.
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.
MPs have been tabling proposed changes to the government’s plans to try to influence the direction of Brexit since the Commons rejected Mrs May’s deal by a record-breaking 432 votes to 202.
The amendments 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.
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.
Mrs May 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 – the insurance policy against a return of a hard border between Ireland and Northern Ireland – 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.”
Senior EU representatives have repeatedly ruled out reopening negotiations with the UK over Brexit, and have insisted the backstop 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 initially 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
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.
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.
The Labour party and 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.
Labour said it was supporting the amendment because the bill it would create could “give MPs a temporary window to agree a deal that can bring the country together”.
But they would “aim to amend the Cooper bill to shorten the possible Article 50 extension”.