The European Commission has said it is “reflecting” on how to offer Theresa May further help to get her Brexit deal through parliament next week.

Brussels has been adamant that it cannot make any actual changes to the controversial deal, but there have been suggestions that further non-binding political “reassurances” could be made to smooth its passage.

“President Juncker spoke last Friday to prime minister May at her request to see how we can help with additional reassurances,” an EU Commission spokesperson told reporters in Brussels.

“Right now we are in the process of reflecting on how to do this and I will update you as soon as there are any contacts foreseen, which is no the case at this stage. But indeed they had agreed to remain in touch throughout the week, which is not yet over.”

But the spokesperson said they could not offer the prime minister a timescale on when help might arrive – raising the prospect that it might come after the vote, possibly helping smooth a second attempt.

The Commission provided some political cover for the prime minister on Thursday however by failing to raise an objection to a eurosceptic amendment that would see MPs given yet another vote in 2020 on whether the most controversial parts of the plan should come into force at all.

The so-called “Swire amendment”, which the government has accepted, would let MPs vote on whether the backstop should come into effect. According to Downing Street the vote would not have automatic legal force, but there would be significant pressure on the government to abandon the backstop if it lost. This action would amount to breaking the withdrawal agreement.

Behind the scenes an EU source told The Independent that it was for the UK government to explain the amendment and that the deal could not be changed.

But publicly a spokesperson would not be drawn on it, telling reporters: “We are not commenting on the on-going parliamentary debate in the United Kingdom.

“I can recall that we have reached a deal with the UK government and this deal is the best and only deal possible and will not be renegotiated so this is where we are at this stage.”

The form any reassurances could take – and whether they happen at all – is still subject to debate and will depend on how the EU reads the situation unfolding in Westminster.

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The Independent reported at the weekend that any further reassurances are not expected to go as far as the full legally binding commitment as demanded by Tory MPs.

Such a text with legal status would require yet another summit – which EU leaders are not prepared to hold after having already been dragged back to Brussels in November for an extra meeting.

Instead, the current thinking in Brussels is understood to be that any further action could take the form of a letter. This would not go as far as Tory eurosceptics have demanded – they want a mechanism for the UK to leave the backstop, or a fixed time-limit.

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The EU already made clarifications to the deal at a Brussels meeting in December where it said the bloc’s “firm determination to work speedily on a subsequent agreement that establishes by 31 December 2020 alternative arrangements, so that the backstop will not need to be triggered”.