Another Conservative Party legislator, Anna Soubry, who opposes the "hard" Brexit that would see Britain leave the European Union without a trade deal in place, said the government's acceptance of the four amendments mean that Rees-Mogg is now effectively "running Britain".
It was not clear the move would fundamentally change her plans - the changes do little more than to put government policy into law, her spokesman said - but it was a victory of sorts for those MPs who say May has betrayed them on Brexit, the biggest shift in British trade and foreign policy for decades.
Eurosceptics will have a chance to show their strength in the House of Commons later Monday by voting on amendments to a bill setting up May's new customs regime after Brexit.
But the early break is likely to spark widespread criticism given that the recess is already scheduled to last for six weeks.
But, if she chooses to fight and then sees a large number of her own party rebel, it would undermine her leadership and cast fresh doubt on whether she can deliver the Brexit plan agreed by her cabinet this month at her Chequers country residence.
The amendments relate to the customs section of the prime minister's Brexit plan, unveiled at a meeting of ministers at Chequers last week.
The report stage of the bill will also see MPs debate a long-awaited amendment that would keep the United Kingdom in the EU customs union post-Brexit that is supported by Labour, the SNP, the Lib Dems and two Tory Remainers, Anna Soubry and Ken Clarke.
Downing Street said it would agree to a wrecking amendment, put forward by Tory rebels, that will affect Mrs May's plans for a new customs partnership with the EU.
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.
Ten Tory Remainers are set to go public with demands for a second vote on Britain's membership of the European Union.
"I wanted the prime minister's Chequers agreement to be a workable compromise", she wrote in The Times.
Former education secretary Justine Greening said other senior Conservatives quietly back a second Brexit referendum.
"It's also quite likely to be either rejected by the European Union or more demands will be made upon it so it will be even less acceptable".
"I have come to the conclusion that it does not respect the referendum result - it is not what people voted for", he said.
While heat from Remain wing of the party has also been turned up, Greening claimed the PM's Brexit plan, contrary to what the she claims, is not what people voted for.
A Welsh Conservative MP has quit as a minister so he could vote against the government on its Brexit Customs Bill.
Another pro-EU lawmaker Dominic Grieve, who has led previous efforts to get the government to soften its Brexit stance, said the party needed to accept compromises "or accept that Brexit can not be implemented and think again about what we are doing".