Allies of Theresa May are drafting a last-ditch plan to rescue her Brexit deal, by offering Tory and DUP MPs a way to avoid being tied indefinitely to EU rules.

Ahead of next Tuesday’s crunch Commons vote, backbench MPs are expected to table a new amendment that more clearly prevents the controversial Northern Irish ‘backstop’ from ever being used.

The amendment would strengthen and update a fresh legislative move adopted this week by ministers to allow the UK parliament alternatives to the ‘backstop’, which seeks to keep the UK locked into European customs rules to avoid border controls in Ulster.

The prime minister is hoping that fresh guarantees and clarifications from Brussels next Monday will help persuade some of her restive Tory MPs to support her proposals for quitting the EU.

But a fresh legal effort on the backstop, which would effectively override the Withdrawal Agreement, is seen as a further way to swing support of Brexiteers.

The “amendment to an amendment” would seek to toughen up the language in a bid by backbenchers Hugo Swire and Richard Graham to help May get her deal through.

The Swire-Graham amendment, which gives MPs a fresh vote on the backstop in March 2020, was dismissed by the DUP last month as “tinkering”, and by Tory MP Steve Baker as “flimsy rubbish”. 

But to win over critics, the wording of their amendment could be substantially strengthened, possibly by removing any option to endorse the “backstop” or by giving MPs the right to say it would “never” come into force.

Nikki da Costa, former No. 10 director of legislative affairs, told HuffPost UK’s Commons People podcast that the idea of a new amendment – which would not be tabled by the government – could help May win more backing.

Referring to Swire’s amendment, she said: “The government find it to be very acceptable. My hunch is people are already saying, the DUP said, I think Steve Baker said, this isn’t really worth enough.

“But maybe you might look at that and you go ‘I’ll add an amendment to that’. The government can’t do that bit or have their hands on it because there will be bits where the EU might cry out against that. 

“But I might look at that and add something else and then maybe you are edging towards being able to pass something which says ‘here’s the recipe guys, EU look at that, see what you can do’.”

On some estimates, the PM is facing the prospect of a rebellion by up to 80 of her backbenchers on Tuesday, but government whips believe the figure will be lower.

The fresh amendment would at least give May the chance to tell Brussels that parliament has come to a view, even if it breaches international obligations. The Swire amendment already raises the prospect of the government ending up in a legal battle with the EU.

On Friday Jean-Claude Juncker signalled that he could offer May help in her attempt to garner support for her deal from MPs. Speaking from Romania for the start of the country’s six-month presidency of the European council, he said: “We, the commission and I, are in touch on a constant basis with No. 10 Downing Street and we will see what happens between now and Tuesday.

“We will see what the British legislature decides to do with the texts that have been put forward. I still hope that here will be a deal. I do not like the prospect of a no deal, which would be a disaster, I think, for our British friends and for the continent of Europeans. And every effort needs to be made between now and Tuesday afternoon perhaps to ensure that this important issue can be resolved satisfactorily.”

Juncker is due to send a letter on Monday offering reassurances to MPs that the Irish backstop would keep the UK in a customs union only temporarily.

Asked about the assurances in the letter, he said: “What we have said very clearly in council and commission, in full harmony, was that there can be no renegotiation, there can be clarification. But that’s all we are discussing with Downing Street what these clarifications might amount to, that should not confused with a renegotiation with regards to the backstop. Aside from these remarks I think it would be unwise to go into the ongoing discussions.”