Earlier on Tuesday Mrs May called on MPs to support the vote to allow her to return to Brussels to reopen negotiations on the Brexit withdrawal deal.
That amendment calls for the backstop to be replaced with unspecified "alternative arrangements" to avoid a hard border in Ireland, and says parliament would support May's Brexit deal if this change were made.
He described the Brexit deal, which was agreed with the European Union but later fell flat in the House of Commons, as a "series of compromises" and said that it was designed around British red lines.
Prime Minister Theresa May said she plans to re-open negotiations in Brussels with an "emphatic message" of what MPs want.
The plan - called the The Malthouse Compromise after Kit Malthouse, the MP who brought the parties together - would lead to Britain leaving the European Union "on time and with a functioning government", former Brexit minster Steve Baker said.
"On behalf of our businesses and the wider food industry we want to highlight to you the challenges for retailers and the consequences for millions of United Kingdom consumers of leaving the European Union without a deal at the end of March", the letter said.
Amendment: This cross-party effort, by Labour lawmaker Yvette Cooper and Conservative politician Nick Boles, would set a time limit beyond which the prime minister would have to ask for an Article 50 extension until the end of the year if no agreement has been struck.
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MPs across all parties had a chance to suggest amendments to her deal, and vote on those too.
But Sarah Wollaston, a pro-EU Conservative, dismissed the plan as "fantasy Brexit".
Instead, the Cooper and Boles plan could now win more backing from politicians who are determined to stop a no-deal Brexit and ensure they have the power to delay the UK's divorce from the European Union if necessary.
Said to be drawn up by Nicky Morgan and supported by others, the plan reportedly "provides for exit from the European Union on time with a new backstop, which would be acceptable indefinitely, but which incentivises us all to reach a new future relationship".
The House of Commons also rejected a bid by Jeremy Corbyn to force a debate on Labour's Brexit plans.
Labour's shadow cabinet met on Tuesday morning to discuss tactics before the Brexit debate in which MPs voted on a range of amendments selected by the Speaker at lunchtime.
"We are extremely concerned that our customers will be among the first to experience the realities of a no-deal Brexit", they added.
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A south wind of 8 to 17 miles per hour will become west in the afternoon, and winds could gust as high as 25 miles per hour . A women battles the heavy wind and snow during a snow storm on March 21, 2018 in Jersey City, New Jersey.
The amendment: A proposal aimed at getting May back to Brussels to renegotiate the Irish backstop has been submitted by Conservative backbencher Graham Brady.
The government hopes to bring the deal back for a new vote in Parliament in February, with enough changes to reverse its thumping defeat on January 15, when lawmakers rejected it by 432 votes to 202.
The EU has said it will not change the legal text agreed with the UK PM.
The lawmakers will also vote on Amendment N which wants alternative solutions to replace the Irish border backstop in the withdrawal deal.
So does she today recognise that the game is up and her only hope is to enter cross-party talks on a soft Brexit deal that could get through the Commons but would destroy her party?
Nigel Dodds, the Westminster leader of the Democratic Unionist Party (DUP) - whose MPs Mrs May's government relies on to win key votes - welcomed the announcement, saying: "From day one. we rejected the backstop and argued for legally binding change within the withdrawal agreement".
European Commission vice-president Jyrki Kateinen said there was "no reason to give any concessions" to the United Kingdom and there was "not much room for manoeuvre" on the backstop.
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Venezuela's President Nicolas Maduro speaks during a news conference at Miraflores Palace in Caracas, Venezuela January 25, 2019. Guaido urged the military, Maduro's most powerful backers, to sever ties with the "dictator" in exchange for an amnesty.
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