SNP MPs would back a new Brexit referendum if it were put to them, party leader Nicola Sturgeon has said.
Campaigners have been pressing for a fresh vote on whatever exit plans result from talks with EU leaders.
PM Theresa May has rejected calls for a so-called People’s Vote and while Labour has not ruled it out, it wants a general election to decide the issue.
Ms Sturgeon said SNP MPs would oppose anything short of staying in the single market and customs union.
Neither choice features in the plan backed by the cabinet at Chequers in July, which the prime minister insists is the only credible option to avoid a “no-deal” scenario.
EU leaders said last month that Mrs May’s proposed new economic partnership “will not work”. However, they have struck a more optimistic note in recent days.
Irish deputy prime minister Simon Coveney said on Sunday that the “chances [of a deal] are good” before the UK is due to withdraw from the bloc on 29 March.
“The withdrawal treaty is already about 90% agreed in terms of text… what is needed now is the two negotiating teams need to lock themselves in a room for the next 10 days or so,” he told Sky News.
The People’s Vote campaign wants the public to have the final say on any deal. On Sunday hundreds of dog-owners marched their pets through central London to support the calls.
Actor Peter Egan and Walthamstow MP Stella Creasy were among those addressing a rally in Parliament Square. Ex-Labour spin doctor Alastair Campbell, who marched with his five-month-old Cavalier King Charles Spaniel, claimed politicians were “scared” of another referendum.
Ms Sturgeon, the Scottish first minister, told the BBC’s Andrew Marr Show that her MPs would back calls for another public vote.
Speaking ahead of the SNP conference in Glasgow, Ms Sturgeon said the UK was heading for a “cobbled together” exit agreement that would be “almost as unacceptable as no deal at all”.
Any deal would be put to MPs in a vote at Westminster, as well as having to be ratified by the remaining EU member states.
“In those circumstances, sensible MPs of all parties should come together to look at the alternative,” she said.
“No doubt calls for a second referendum would grow in those circumstances, and I’ve said before we wouldn’t stand in the way of a second referendum. I think SNP MPs would undoubtedly vote for that proposition.”
Analysis by BBC political correspondent Nick Eardley
In an age of political shocks, Nicola Sturgeon backing a new EU referendum won’t count as one of the biggest.
The party had always said it was open to the idea, even if it still has concerns you could end up with another situation where Scotland votes Remain, but ends up bound by a UK-wide result.
It makes the SNP – with its 35 MPs – the biggest party in Parliament to back a so-called “people’s vote”.
But the Commons numbers who have committed to supporting one still remain a small minority.
The government has ruled one out. Labour says it’s still an option – but it isn’t their preference.
So campaigners who want the public to have its say on the final deal still have a lot of work to do if they are to get their wish.
SNP conference begins
Thousands of delegates are gathering at the Scottish Event Campus in Glasgow for the SNP conference, which will include motions on reusable plastic, compulsory CPR training in schools and the devolution of migration policy.
Speaking on Sunday, Joanna Cherry MP said Scotland would not necessarily have to have a second independence referendum to leave the United Kingdom.
The SNP’s home affairs spokeswoman at Westminster suggested independence could be achieved through a “democratic event”, like a general election.