The DUP has backed the so-called "Malthouse" alternative proposals to the draft Brexit withdrawal agreement.
The compromise plan is the result of talks co-ordinated by MP Kit Malthouse between MPs from the Leave and Remain wings of the Conservative Party.
The plan involves a "recasting" of the Northern Ireland backstop as "free trade agreement-lite" with a commitment on all sides there should be no hard border on the island of Ireland and an extended transition period to December 2021.
DUP MPs have backed the plan following a meeting on Tuesday morning.
DUP leader Arlene Foster said: "The DUP has given its endorsement to the plan. We believe it can unify a number of strands in the Brexit debate including the views of remainers and leavers.
"It also gives a feasible alternative to the backstop proposed by the European Union which would split the United Kingdom or keep the entire United Kingdom in the Customs Union and Single Market.
"Importantly, this proposal would also offer a route towards negotiating a future trade relationship between the United Kingdom and the European Union.
"If the Prime Minister is seeking to find a united front, both between elements in her own party and the DUP, in the negotiations which she will enter with the European Union, then this is a proposition which she should not turn her back on.
"There is no better time to advance this alternative given the confusion and disarray which is now manifesting itself in Brussels. This has been displayed both by the contradictory EU statements and the panic stricken behaviour of the Irish government.”
Former Cabinet minister Nicky Morgan said discussions had been taking place for “some days” between herself, health minister Stephen Hammond, and Solicitor General Robert Buckland on one side and Jacob Rees-Mogg and Steve Baker from the ERG on the other.
"The Prime Minister has been aware of the discussions. At some point there has to be compromise on all sides in order to get a deal over the line. That is what most of us want to see – a negotiated settlement with the EU,” Ms Morgan told the BBC Radio 4 Today programme.
“People like me want to avoid a no-deal outcome, a crashing out on March 29. We have to look for ways to do that. We are all prepared to compromise on that.”
Former party leader Iain Duncan Smith, from the Brexiteer side, said the plan represented the “best hope” for the Conservatives.
“I really urge the Government to embrace this because what this will tell the European Union is that now, I believe, a majority of Parliament, particularly in the governing party, have agreed there are compromises to be made,” he said.
However, International Trade Secretary Liam Fox said: “There are all sorts of ideas being put out, but Parliament cannot take a decision unless it is on the order paper and it is not on the order paper.”