In an admission that some countries have sought to extract a high price for their continuing to trade with Britain after leaving the EU, Liam Fox, the worldwide trade secretary, said some nations had made the requests as part of talks.
The group including Labour MP Yvette Cooper and Tory former ministers Sir Oliver Letwin and Nick Boles said their plan was created to prevent the country drifting into a no-deal Brexit "by accident".
On Tuesday, May urged lawmakers to give her more time, promising Parliament yet another series of votes on the next steps in the Brexit process on February 27 if she has not secured changes to the Brexit deal by then.
However, influential Brexiteers from the European Research Group of Tory backbenchers are angry at being asked to support the PM's motion. "We want to leave with a deal and that is what we are working for".
The Scottish government has stepped up its preparations for a no-deal Brexit as it again called on Theresa May to rule out the possibility.
His interpretation was denied by Mrs May's spokesman who said: "No-deal is an eventuality we wish to avoid, but one we continue to plan for".
"It is the only way of giving the House of Commons the time to produce a consensus about a positive way forward if the PM can not get her deal through by mid-March".
Ms Sturgeon said it was "reckless and negligent" for the United Kingdom government to refuse to rule out no-deal, adding: "But we appear to be dealing with a United Kingdom government that's prepared to act recklessly and negligently".
The United Kingdom is on course to leave the European Union on March 29 without a deal unless May can persuade the bloc to amend the divorce deal she agreed a year ago and get it approved by British lawmakers.
"Countries like Japan and South Korea and others are going to expect better terms from the United Kingdom, at the expense of the United Kingdom, than they've had to give to the European Union", he said.
If a deal is agreed, MPs will have a second "meaningful vote", more than a month after Mrs May's deal was rejected in the first one.
The prime minister has promised to return to the Commons on 26 February with a further statement - triggering another debate and votes the following day - if a deal has not been secured by that date.
Addressing the House of Commons a fortnight after MPs voted for her to go back to Brussels and replace the controversial Irish border backstop, Mrs May acknowledged that she would need "some time" to hold talks with the EU. The U.K.'s bid for last-minute changes has exasperated European Union leaders, who insist the legally binding withdrawal agreement can't be changed.
Veteran Tory Europhile Kenneth Clarke has tabled a further amendment, backed by senior figures from across the House including Harriet Harman, which would allow MPs to vote for their preferred Brexit outcome.
Brexit Secretary Stephen Barclay said Wednesday the government is not planning a delay, saying "the prime minister has been very clear that we are committed to leaving on March 29".
"That is just the facts of the case", he told BBC Radio 4.
He declined to say whether Labour MPs would be disciplined for disobeying the whip in upcoming Brexit votes.