MPs in the lower House of Commons will vote on a raft of amendments produced by the upper House of Lords, which May claims would weaken the government's hand in exit talks with the EU.
He said Mrs May promised to table amendments in the House of Lords that will address their concerns.
In practice, the amendment would give MPs and Lords the power to decide what happens should they decide to reject the Brexit deal May hopes to bring back from Brussels later this year.This means MPs and Lords could tell May to go back to negotiating table and get something better.
Remain-backing former minister Anna Soubry insisted that Mrs May had agreed at Tuesday's meeting to discuss all elements of Mr Grieve's amendment - including the measure to allow MPs to take control of the process if no Brexit deal is struck by February.
The parts of his amendment which he expects to be taken forward by ministers provide a mechanism by which Parliament has to be consulted by the end of November in the event of no deal or if a proposed agreement is rejected, he said.
"I'll vote for the EEA amendment because we need to keep our options open", he told lawmakers.
Speaking in parliament on Wednesday, May said the government could never allow the hands of the government to be tied in the negotiations or allow the Brexit decision to be reversed.
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Ministers - who have accepted just one of the 15 amendments to legislation - are confident of winning most of the votes when the bill returns to the Commons on Tuesday and Wednesday.
He added: "I understand the difficulties MPs representing constituencies which voted strongly for Leave or Remain have on the EEA amendment".
But she faces a gruelling bout of "parliamentary ping-pong" with the Lords, as the Bill bounces back and forth between the two Houses over the coming weeks.
Lawmakers kicked off two days of debate on Tuesday on changes to May's Brexit blueprint, or European Union withdrawal bill, after the upper house of parliament, the House of Lords, introduced 15 changes.
It is not clear whether that will win over potential rebels.
Speaking on BBC radio on Tuesday morning, Mr Davis said a meaningful vote would not lead to Britain staying in the EU.
But the resignation by Phillip Lee, who has always been critical of the government's Brexit strategy, underlined the deep rifts in the party over Brexit that makes such votes anything but easy.
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The Manchester United forward has more energy tracking back and when he attacks he can go past people with the ball at his feet. "I think that only puts us in good stead for this tournament and future tournaments".
"Our policy is to leave the customs union so we can conduct our own independent trade policy, but it would be appropriate to have an arrangement in place", Baker told reporters.
He said: 'If, in the future, I am to look my children in the eye and honestly say that I did my best for them I can not, in all good conscience, support how our country's exit from the European Union looks set to be delivered'.
In a headache for leader Jeremy Corbyn, however, 75 Labour MPs rebelled against his order to abstain on the vote, including five who quit their jobs in the shadow cabinet.
It's an amendment that calls for the government to "take all necessary steps to implement an global trade agreement which enables the U.K.to participate after exit day in a customs union with the EU in the same terms as existed before exit day".
After days of division and bitter rows between Brexiteers and Remainers in the Tory ranks, Theresa May was able to see off another amendment that would have tied Britain to the customs union post-Brexit by 325 votes to 298, majority 27.
May is expected to address a meeting of Conservative members called the 1922 Committee later on Monday and will repeat her stance that the European Union withdrawal bill is purely technical "to ensure a smooth and orderly transition as we leave".
But Tory MP Andrew Bridgen, a leading Brexit backer, said the concessions could "come back to haunt" the government if they amounted to a veto over the terms of the UK's departure.
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