DUP leader Arlene Foster yesterday joined forces with former Brexit secretaries David Davis and Dominic Raab to push for changes to the withdrawal deal.
At an event in the British Academy in central London, DUP representatives appeared with high-profile Brexiteers to launch the 'A Better Deal' pamphlet, which sets out proposals for an alternative EU withdrawal agreement.
On Twitter, Mrs Foster wrote: "Delighted to speak at the launch of A Better Deal. The WA would undermine the economic & constitutional integrity of the UK. There are alternatives.
"London, Dublin & Brussels have all ruled out a hard border in any circumstance. Backstop is not needed."
Included in the document is a proposal for a new protocol on Ireland/Northern Ireland to replace the backstop.
The document states that "nothing in the New Protocol on Ireland/Northern Ireland shall imply the creation, existence or maintenance of a single customs territory between the European Union and the United Kingdom".
The protocol would be in place from the end of the transition period at the end of 2020 if no alternative arrangements are in place to guarantee the absence of a hard border.
The paper 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 said that Parliament had effectively rejected the deal by making it impossible for Mrs May 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, extendible 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 added: "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."