Some members of May's cabinet are reported to be pushing for a second vote, but the prime minister is against the move, warning it "would do irreparable damage to the integrity of our politics."
It is also unclear what options to give people in a second ballot -- and what happens if Brexit wins again.
- Parliament votes on options -
Another possibility that has come to the fore in recent days is for several non-binding votes to be held in parliament on different Brexit options to effectively determine the government's strategy.
The first would be on May's deal but others could include a no-deal Brexit, a second referendum or a "Norway deal" that would keep Britain much more closely anchored to the European single market and allow unfettered immigration.
Business secretary Greg Clark appeared to hint at this on Monday, telling BBC radio that parliament should be "invited to say what it would agree with" if it votes against the draft Brexit agreement on the table.