May's premiership has been left hanging by a thread following the dual resignations of Brexit minister David Davis and Foreign Secretary Boris Johnson from her Cabinet.
Theresa May clinging on to power after Boris Johnson quits over Brexit plans.
"I think you have to give all the protagonists, whether it's the president or the prime minister, a little bit of leeway here".
A third amendment would require the government to sign up to having a separate Value-Added Tax regime from the EU, while a fourth would oblige the PM to creating primary legislation if she wanted to remain in the EU's customs union.
"Top-level cabinet resignations usually spell trouble for a government and Boris Johnson's might well have led to a leadership challenge, but May appears to have emerged unscathed from a meeting of her party, for now", said Al Jazeera's Jonah Hill, reporting from London.
"There was always going to be a moment in time that was needed for the British Prime Minister to show her authority because she had a very divided cabinet on her approach to Brexit".
But Johnson, a leading Brexit campaigner, said following European Union rules without being able to alter them risked consigning Britain to the "status of colony", and said it looked like a "semi-Brexit".
"I don't believe it was possible to move the Brexit negotiations forward without having that moment when the majority of the conservative party were willing to face down the hard-line Brexiteers", said Mr Coveney.
Speaking at the Institute of global and European Affairs in Dublin, Minister Coveney said there had not been a clear British negotiating position for many months.
Under party rules, 48 Tory MPs - 15% of the party's 316-strong representation in the Commons - must write to the chairman of the backbench 1922 Committee, Sir Graham Brady, to trigger a no-confidence vote.
Labour's deputy leader, Tom Watson, mocked the former foreign secretary, saying he had "a career ahead of him on Love Yourself Island".
The ex-MP said there was a "plan" to curtail the role of the Brexit department.
On Thursday, the government proposal or White Paper was due to be published, setting out the terms for Britain's exit from the European Union and its future relations with the bloc after March 2019.
Britain would leave the EU's single market and customs union as planned, to end free movement of people and sign its own non-EU trade deals.
Johnson has so far remained out of the spotlight since he resigned, and there has been little comment from potential leadership contender, leading pro-Brexit lawmaker, Jacob Rees-Mogg, who has been critical of May's proposals.
He said Brexiteers need to accept that pursuing a hard Brexit would likely fail to clear the Commons, risk thousands of job losses and threaten peace in Northern Ireland.
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