The deal reflects Switzerland's "mind the gap" strategy of ensuring seamless trade ties with Britain, regardless of whether London is able to strike and approve a formal exit agreement with Brussels by March 29, the date it is scheduled to leave.
An attempt by Labour lawmaker Yvette Cooper and Conservative Nick Boles to give parliament the power to request a delay to Britain's March 29 exit was defeated by lawmakers on January 29, but Boles said he would renew that effort on February 14 if a deal has not been passed by then.
British government asked lawmakers on Sunday to give Prime Minister Theresa May more time.
She'll say that if she hasn't brought them new deal by February 27, there will then be another opportunity to vote, Communities Secretary James Brokenshire confirmed in an interview.
May will promise lawmakers a second opportunity to influence the Brexit talks later in the month in a bid to stave off any rebellion from within her own party by those who fear Britain could end up leaving without a deal. "There needs to be a day when Parliament says that's it, enough is enough".
MPs voted to replace the controversial backstop with "alternative arrangements" in a vote on amendments to the PM's Brexit deal last month.
The British government is seeking to win more time to secure European Union concessions on Brexit that could pass parliament and avert a chaotic split from the bloc on March 29.
The move led to a backlash from pro-EU Labour MPs, but Starmer defended the approach and warned against a split in the party.
The government has not ruled out supporting this - and has promised a formal response to it and further talks with Labour - but they say it would prevent the United Kingdom from making its own trade deals after Brexit.
Treasury chief secretary Liz Truss refused to rule out quitting if May did accept the demand for a customs union.
She told Sky News' Sophy Ridge On Sunday: "I appreciate Jeremy Corbyn has come to the table but the reality is what he is proposing does not deliver on what we want as a country".
May and her government have repeatedly said membership of a customs union would prevent it having an independent trade policy - something they have promoted as one of the main economic benefits of leaving the EU.
Mrs May described discussions with European Union leaders in Brussels as "robust but constructive" and insisted she was determined to "negotiate hard" over the coming days to secure legally-binding changes to the Agreement which will render it acceptable to Parliament.