Mr Grieve had originally wanted the amendment to say that the government must seek the approval of Parliament for its course of action - and that ministers must be directed by MPs and peers in the House of Lords.
The Prime Minister is facing the biggest parliamentary bust-up yet on her flagship Brexit legislation after a compromise created to keep critics in her own party on board was denounced as "unacceptable" by Tory Remainers.
Some Leavers were anxious MPs would vote down the deal and then instruct the Government to keep the United Kingdom in the Single Market or customs union - or perhaps the EU entirely.
Mr Tugendhat suggested there was no need to "beef up" the "meaningful vote" which now offers parliament the choice between the government's deal and Britain leaving the European Union with no deal.
Mr Grieve previously tabled his own proposals, which would have allowed Parliament to dictate the next steps the Government should take if no deal was reached by the end of February.
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Rome also summoned the French ambassador over the dispute - the second time it has done so over the migrant crisis in two months. This has placed a significant burden in recent years on the countries where most undocumented migrants arrive.
However, the Grieve amendment was not forced to a vote on Tuesday after would-be rebels accepted "personal assurances" from the PM that a compromise would be found.
However, the vote will not give Parliament an explicit veto on Britain leaving the EU without a deal, which is contrary to what pro-EU MPs - including a powerful group of Conservative "rebels" - say they were promised by the prime minister this week.
The ping-pong process of the withdrawal bill between the two houses of parliament returns to the Lords on Monday, when peers are expected to reject the amendment drafted by May and her team, and insert one modelled more closely on Grieve's idea.
The government's amendment to the EU Withdrawal Bill sets out what must happen if the prime minister announces - before 21 January 2019 - that no deal has been reached with the EU either on the withdrawal agreement or the future relationship.
Pro-EU Tories were quick to voice their anger.
Speaking on why she voted against the government, Soubry tweeted "I voted in favour of the Lords amendment because I feared she would not be able to deliver on her promise because she won't see off the no deal hard Brexiteers".
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The front seats also feature a "semi-electric" fold function to make it easier for rear occupants to get in and out of the coupe. Built at the brand's Dingolfing plant, which also produces the 7 Series , the 8 Series is expected on the roads from November.
"We could collapse the government, and I can assure you I wake up at 2 a.m.in a cold sweat thinking about the problems we have put on our shoulders", said Dominic Grieve, the lawmaker negotiating with the government on the final wording of the laws that will end Britain's European Union membership.
"Grateful for the conversations but without consultation what was agreed earlier today has been changed", she said.
"Would be amusing if only it wasn't such a serious issue".
Labour's shadow Brexit secretary Sir Keir Starmer told the government their amendment is "simply not good enough".
"If the government can't get the most important treaty through Parliament we'll be looking for a new government", said Mr Tugendhat. "Parliament can not - and should not - accept it".
On Wednesday, the amendments will return again to the Commons, where May faces the possibility of defeat over a meaningful vote.
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And they're doing it for different reasons. "The great part about sports are the relationships". I've been with guys from all different parts of the country: Every colour, race, belief.
Tory MP Sarah Wollaston, who had planned to rebel on Tuesday but was bought off by the Prime Minister, took to Twitter to express her disappointment.