To secure any changes, the British prime minister faces European Union leaders who, until now, have not shown willing to touch the Irish backstop.
UK Prime Minister Theresa May on Tuesday said she would return to Brussels to secure a new deal without the controversial "backstop", designed to ensure a hard border could never appear on the island of Ireland.
It came after MPs passed an amendment to removing the backstop from the withdrawal agreement and asking May to come up with "alternative arrangements" to avoid a hard border.
However, to secure any changes, the British prime minister faces European Union leaders who, until now, have not shown willing to budge on the issue.
May admitted that there was "little appetite" in Brussels for renegotiation, a point confirmed shortly afterwards by EU council president Donald Tusk who described the deal rejected by MPs as the "best and only way to ensure an orderly withdrawal."
What's more, Simon Coveney, Irish deputy prime minister, described the backstop as "part of a balanced package that isn’t going to change," on BBC One’s The Andrew Marr Show.
You can see EU leaders and Irish Taoiseach Leo Varadkar's previous comments on the backstop in the above video player.