A cross-party group has been holding secret talks to draw up a fresh version of an amendment tabled by Labour MP Yvette Cooper to extend article 50.
The move, expected to be announced this evening, comes after the Prime Minister asked the Commons for another fortnight’s grace to continue talks with the EU.
Mrs May said she needed more time but confirmed they would get another chance to have their say in votes on Brexit on February 27.
But the Remainer MPs want to put her on notice that she will not be able to delay her Brexit “high noon” beyond that point.
The Mirror has learned that Ms Cooper plans to table a Brexit amendment along with Tory grandee Sir Oliver Letwin today or tomorrow.
But the pair are NOT expected to put their proposal to a vote until the end of the month – their best chance of getting it through Parliament.
One source told the Mirror: “In terms of maximising Tory support for the plan, it’s clear they want to give her one final opportunity to get her deal.
“So it’s likely that it will be put to a vote at the end of the month, rather than now. At that stage, there are likely to be Tory resignations over it.”
Ms Cooper and Mr Letwin’s plan would remove the time limit for delaying Brexit Day from an earlier version of the amendment, which was defeated by MPs in January.
Instead it would make the PM decide the length of the extension she would be forced to request from Brussels.
Mrs May would also be compelled to give MPs a formal vote before crashing out of the EU without a deal.
A handful of Remainer ministers have pledged to quit Government if the PM adopts a no deal Brexit policy – or appears to be slipping towards one.
They are thought to include some in Mrs May’s own cabinet including Justice Secretary David Gauke, Work and Pensions Secretary Amber Rudd and Business Secretary Greg Clark.
The Commons rejected an earlier amendment by Ms Cooper that would have forced the PM to ask Brussels for a formal extension to article 50.
The shock defeat, 321 votes to 298, came as a crushing disappointment for Remainers who widely expected to block a damaging no deal Brexit.
Despite support from the Labour front bench, 14 Labour rebels turned against the amendment, balancing out 17 Tory rebels voted in favour of delaying Brexit.
One of their key concerns was a suggested delay of nine months in the planned bill. The Labour party agreed to back the move if that was brought down to three months.
Ms Cooper has insisted throughout that her aim has been to give the Government more time to negotiate a deal, rather than an attempt to stop Brexit.