MPs are set to take back control of the Brexit agenda today in a fresh attempt to find an alternative to Theresa May's deal that Parliament can support.

The Commons will stage a second round of "indicative" votes later today on a series of rival proposals tabled by backbenchers to see if any can command a majority.

The move comes as Mrs May struggles to contain the rising tensions with her Cabinet as the clock counts down to the latest EU deadline on April 12.

Despite seeing her deal again defeated on Friday, the Prime Minister is determined to bring it back to the Commons for a fourth time - possibly as early as Tuesday - in a final roll of the dice to get it over the line.

Mrs May spent the weekend trying to build support among MPs who could be won over, with aides saying she was "100% focused" on getting the result she needed.

Some in Parliament believe that if MPs begin to coalesce around a "softer" Brexit in Monday's votes, it may finally convince Brexiteer hold-outs that the PM's deal now represents the "hardest" break with the EU available.

READ MORE: Here are all the motions MPs will be voting on

The pro-EU Justice Secretary David Gauke warned Mrs May not to ignore the will of Parliament if it does swing behind a "softer" deal such as the customs union plan proposed by Tory veteran Ken Clarke, which came closest to gaining a majority in the first round of indicative votes.

And in an interview with the BBC, Tory chief whip Julian Smith said that the Parliamentary arithmetic means a "softer type of Brexit" is inevitable.

The Prime Minister has, however, set her face firmly against a customs union, warning it runs counter to the Conservatives' election manifesto and would inhibit Britain's ability to strike trade deals around the world.

If she were to give way, she would provoke a furious reaction from Brexiteers, with International Development Secretary Penny Mordaunt and Transport Secretary Chris Grayling among the ministers reportedly ready to resign.

Mr Gauke, meanwhile, said at the weekend that he would quit if Mrs May took Britain out of the EU without a deal, with other senior pro-EU ministers likely to follow suit.

His warning followed a letter to the Prime Minister signed by 170 Tory MPs demanding Britain leave by May 22 at the latest "without or without a deal".

In a sign of her waning authority, it was written by Brexit Minister Chris Heaton-Harris, according to The Times.

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Meanwhile, Jeremy Corbyn sought to keep up the pressure, hinting that Labour could table a fresh vote of no confidence in the Government in a bid to force a general election.

"We're ready for a general election, whenever it comes," he told the Daily Mirror.

"A general election would give us the chance to remove this incompetent and failed Tory Government."

Amid the continuing Cabinet turmoil, eight motions have been tabled in the latest indicative votes, with Speaker John Bercow set to announce which he has selected for debate.

As well as Mr Clarke's customs union plan, there are again motions calling for a "softer" Norway-style arrangement, dubbed Common Market 2.0, and a confirmatory referendum on any deal that is agreed.

With horsetrading between the various groups continuing over the weekend, some supporters of Common Market 2.0 were hoping to win over the DUP, arguing their plan would avoid the need for the Northern Ireland backstop.

They were encouraged after the deputy leader of the pro-Brexit party, Nigel Dodds, said he would rather remain in the EU than back Mrs May's deal.

Mr Bercow is also expected to say whether MPs will adopt a preferential voting system this time around to help whittle down the options.

Meanwhile, with potential successors to Mrs May beginning to jostle for her position following her announcement that she will quit once she has finally delivered on Brexit, Mr Grayling suggested the next leader should be a senior figure who campaigned for Brexit.

He indicated that the younger generation of contenders - which includes Dominic Raab, Liz Truss and Matt Hancock - should wait until after the next general election due to take place in 2022.

"The next two or three years are going to be very tough because the European stuff is not going to go away," he told The Daily Telegraph.

"We have got to negotiate a free trade agreement, sort out where we are, but also as we get into the 2020s, we are going to have to pass the torch to a new generation.

"Is the person who takes us through the next two or three years and sorts out Brexit and gets the sort of hard time that Theresa has had, the same person who we want to be leading us into the 2027 general election?"