The amendments to be voted on Monday are unlikely to pass without Labour support, but they represent a show of power by Brexiteer MPs toward the prime minister.
The statement came not long afer a Conservative Party MP and former cabinet minister said in an interview that the British public should be consulted in a new referendum on whether Britain should leave the European Union.
Business minister Greg Clark urged party members to get behind the prime minister's plan: "When it comes to Parliament, I hope and expect that it will be persuasive that what is on offer will be good for the United Kingdom, it would be good for every part of the U.K".
The government's acceptance of the amendments to the Taxation (Cross-border Trade) Bill, or customs bill, also did little to ease the tensions in May's party, which is at war with itself over the Brexit plans. "We'll have an idea of the numbers, I suppose, at 10 o'clock on Monday evening".
Eurosceptic MPs had targeted her government's customs legislation to try to toughen up her plans to leave the European Union, but instead of facing them down and fuelling tensions, her spokesman said the government would accept their four amendments.
It was unclear whether they will actually press them to a vote after some pro-EU MPs backed Mrs May's Chequers plan and EU white paper.
From the other wing of May's party, pro-EU former education minister Justine Greening called on Monday for a second referendum, saying it was the only way to break the stalemate in parliament over the best future relationship with the bloc.
Putin summit kicks off in Helsinki
Frankly, we have not been getting along very well for the last number of years. "Whoever says we are foes is spreading fake news". Trump also said that "getting along with Russian Federation is a good thing, not a bad thing".
That's unacceptable. The only solution is to take the final Brexit decision out of the hands of deadlocked politicians, away from the backroom deals, and give it back to the people.
She will also announce £343m in additional research and development funding, including investment in new "cleaner and greener" electric aircraft technology.
On BBC Radio 4's Today programme he urged Tory colleagues who "want to get on with Brexit" to acknowledge that the Bill was "essential" and should not be impeded.
"I am not prepared to compromise their wishes to deliver a watered down Brexit".
Mrs May's spokesman claimed this afternoon that she had accepted to rebel amendment because it was "consistent" with her Chequers proposals.
"I suspect the Chequers deal is, in fact, dead", Conservative lawmaker Bernard Jenkin told the BBC.
"I'm afraid it is neither beloved by Remainers or Leavers".
Pro-Europeans also dislike May's plan, particular her goal to have looser ties with the European Union for Britain's dominant services sector.