Tory Brexiteers have launched a pamphlet setting out proposals for an alternative EU Withdrawal Agreement.
The paper, entitled A Better Deal, retains many elements of Mrs May's package but removes what they referred to as "poison pills" which prevented her securing cross-party support.
Backers of the new approach - including former Brexit Secretary Dominic Raab - said that the British Parliament had effectively rejected the PM's deal by making it impossible for her to get it through the Commons.
The document, drawn up by a former adviser to Liam Fox, Shanker Singham, customs expert Hans Maessen and lawyer Robert MacLean, proposed:
- No single customs territory between the UK and the EU, allowing Britain to regain control over tariffs and regulations and negotiate trade agreements with other countries;
- A 10-year, extendable backstop featuring advanced customs facilitation measures to keep the Irish border open, a zero-tariff free trade agreement in goods and a commitment by all parties not to place infrastructure on the border;
- Mutual recognition of regulations, with measures to ensure that the animal health and disease control zone on the island of Ireland can be maintained;
- Level playing field provisions on labour, the environment, competition and state aid;.
- The removal of geographic indications provisions from the Withdrawal Agreement, to be considered as part of a later free trade deal;
- The removal of language on World Trade Organisation collaboration, ensuring that the UK can operate independently in the WTO.
Launching the paper, former Brexit secretary Dominic Raab said: "There are modest and reasonable changes that could help salvage the proposed deal with the EU.
"The UK needs a unilateral exit mechanism from the backstop, but we can give the Irish Government assurances that we would put in place specific measures to guarantee no return to a hard border."
"This proposal can help deliver this and allay fears that the UK would be stuck indefinitely in an undemocratic regime of laws we have no control over and can't exit."
Also backing the paper was Mr Raab's predecessor as Brexit secretary David Davis.
Labour MP David Lammy, a supporter of the Best for Britain campaign for a second referendum, said: "The alternative plan of two failed Brexit secretaries is not a solution but a recipe for disaster.
"Not only would it create a hard border in Ireland, it would cut the UK off from our closest partners and make the whole country poorer, disproportionately hurting the worst off.
"As we stand, there is no clear majority in this House for any specific Brexit plan. The way to unblock our politics and get a mandate for a tangible plan to move forward is through a people's vote, which gives the option to remain in the EU."
