The weekly meeting of the Cabinet on Tuesday is expected to sign off on a package of measures to be included in the forthcoming Withdrawal Agreement Bill (WAB) aimed at winning cross-party support.
However there was widespread scepticism at Westminster that it will fare any better than her three previous failed attempts to get the Commons to pass the deal.
Following the collapse last week of cross-party talks with Labour aimed at reaching a common approach, Jeremy Corbyn said he had not yet seen anything new that would persuade him to support it.
It comes at the start of what looks likely to be another torrid week for the Prime Minister with the Conservatives braced for a hammering at the hands of Nigel Farage’s Brexit Party in the European elections on Thursday.
One weekend poll put them in a humiliating fifth place behind the Greens, with the results likely to exacerbate frustration in the party at the failure to leave the EU in March as planned.
Labour - which has been criticised for facing both ways on a second referendum - is also expecting a difficult result with the same poll showing them in third place behind the Liberal Democrats.
A Government source said the WAB - which is needed to ratify the deal with Brussels - would include new measures on protecting workers’ rights, an issue where agreement with Labour was said to have been close.
However, the source made clear the package would not just be aimed at Labour MPs but would seek to secure the widest possible support across the Commons.
It is expected to include provisions on future trade arrangements with the EU, on environmental protections, and on Northern Ireland, including the use of technology to avoid the need for border controls with the Republic.
Ministers will also consider whether to put any of the alternative approaches to indicative votes in the Commons to establish which, if any, can command a majority.
It will not, however, seek to re-open the Withdrawal Agreement - which included the controversial Northern Ireland “backstop” - after the EU repeatedly made clear it could not be re-negotiated.
Mrs May has said she will bring the WAB before MPs for its second reading vote in the first week of June following the short Whitsun recess.
Regardless of how the vote goes, she will then meet the chairman of the Tory backbench 1922 Committee, Sir Graham Brady, to agree a timetable to elect her successor as party leader, paving the way for her departure from No 10.
The Prime Minister expected to set out details of her WAB proposals in a major speech before the end of the month.