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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." [...]