Crucially, ministers have conceded that if MPs vote down the Withdrawal Agreement with Brussels, that will not result in the United Kingdom crashing out of the European Union with no deal - a scenario that few MPs would countenance because of the significant economic damage it would entail.
The UK government is talking about a backstop agreement too, but it is referring to what customs arrangement could be put in place for the whole of the UK until a new post-Brexit customs deal is up and operational.
And senior pro-EU Tory Dominic Grieve withdrew his own amendment, which would have given MPs powers to dictate what the Government should do if no acceptable agreement is reached by February 2019.
Mr Grieve warned that if the Government failed to offer an adequate compromise, it would not be "the end of the matter".
But the Prime Minister is likely to face the risk of further rebellions further down the line.
While Conservatives at Westminster say some of these must come to Parliament to allow for common frameworks to be established in areas such as agriculture and environmental regulations, ministers at Holyrood fear the powers of the Scottish Parliament could be restrained for up to seven years.
The British government was rocked by a resignation and faced anger in Parliament over its Brexit plans, but staved off defeat by offering concessions to lawmakers who want to soften the terms of the UK's exit from the European Union.
May hopes to resolve the border issue with a wider trade deal between the European Union and Britain, but has agreed to the need for a plan B if this is delayed or does not happen. Both sides say they do not want a hard border because the open frontier is part of the Good Friday Agreement, which brought an end to the Troubles, reported the Independent.
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He said the USA is working on the issue with South Korea, and Japan-as well as with China , but "to a lesser extent". Murphy, have been quick to point out that no long-term verification process was included in the agreement.
Remainer Stephen Hammond said a group of potential rebels - believed to number 15 to 20 - received assurances from the PM moments before the key vote.
"It was the Prime Minister's personal assurance that was very important to us, and she has given us that".
Lawmakers were told to back that amendment rather than one on the EEA, an order some pro-EU Labour politicians said they would defy.
Frank Field, a veteran lawmaker from the northwest of England, was his first victim after suggesting the point of the amendment Pennycook was backing was to stop Brexit, then Gareth Snell, who represents Stoke-on-Trent in the Midlands, got the same treatment for making a similar point.
Earlier during prime minister's questions, Mr Corbyn taunted Mrs May by asking if she agreed with comments by her foreign secretary Boris Johnson that Donald Trump would do a better job at Brexit negotiations.
Welcoming the move, a Labour spokesperson said: "Labour has repeatedly emphasised that Brexit can not lead to a hard border in Northern Ireland or any disruption to the North-South cooperation guaranteed by the Good Friday Agreement".
Liberal Democrat Brexit spokesman Tom Brake said: "As has become a tradition in Brexit negotiations, the Tories have been forced to cobble together a compromise".
"It buys the Government more time, and has no doubt bought off some of the serious concerns of MPs, but this can't just be a case of kicking the can down the road and forgetting about it".