The four amendments to the crucial Customs Bill were put down a day before Thursday's publication of a White Paper setting out the British prime minister's plans, which infuriated Leavers and prompted the resignation of Cabinet ministers Boris Johnson and David Davis.
Following Mr Johnson and Mr Davis's resignations, two deputy chairmen of the Conservatives - Ben Bradley and Maria Caulfield - quit their posts on Tuesday, claiming the PM's proposals would not harness the benefits of Brexit.
Andrew Bridgen became the first Conservative MP to publicly confirm he had sent a letter calling for a vote of confidence in the prime minister, it was reported.
British trade minister Liam Fox said on Wednesday he did not believe that Britain's new Brexit strategy would inhibit its ability to agree trade deals with countries around the world, after two cabinet colleagues resigned over the policy.
Other amendments would force Britain to have a separate Value-Added Tax regime from the EU and ensure the Prime Minister has to table primary legislation if she wishes to keep Britain in the customs union.
The resignations have plunged her government into a crisis that could challenge her leadership and result in a no-confidence vote in parliament.
It led to a string of resignations from pro-Leave campaigners, including former senior Cabinet ministers Boris Johnson and David Davis.
"I can not support the direction of travel in the Brexit negotiations", she added.
Fast-forward a few days and Brexit hardliners are on the defensive, while the government is showing a willingness to compromise and outlining a more pragmatic vision for a country half-in, half-out of the European Union.
Labour's deputy leader, Tom Watson, mocked the former foreign secretary, saying he had "a career ahead of him on Love Yourself Island".
"Nor do we expect a leadership challenge".
Tories unhappy with the current Brexit plans need to accept the "harsh truth" that there's no other option, William Hague has said.
Her plans, which also argue for Britain to set its own trade tariffs and open up services markets, are an attempt to meet the demands of businesses, pro-EU voters, Brexit supporters and the European Union, which has warned repeatedly that time is running out.
He had said: "The Government's commitment at Chequers to the political and constitutional integrity of the United Kingdom with no borders between Northern Ireland and the rest of the United Kingdom is a welcome reaffirmation of what is an absolute priority for us".
"Mrs May has recognised that the only pragmatic approach to decoupling from the European Union is a softer version of Brexit", the Financial Times said in an editorial.