May’s de-facto deputy David Lidington has held advanced talks with senior Tories and opposition MPs to explore ways MPs could be given a say on the next stage of the process. Those familiar with the talks said he appeared to be speaking with the prime minister’s authority.

Greg Clark publicly broke ranks on Friday to say the government should keep its promise to facilitate a process to find a majority for a compromise in parliament.

“There’s no reason why the government should be forced to do something that it is committed to do anyway,” the business secretary said.

However, the mood has hardened among some of the initiative’s supporters who have lost trust in the government to decide which options should be put to MPs, and fear a “stitch-up” where choices are set up to fail.

May must start her gruelling week on Monday by making a statement to MPs on Brexit, before facing an amendable motion on the way forward.

A key amendment, tabled by Oliver Letwin, Hilary Benn and Dominic Grieve, would set aside Wednesday for MPs to take control of House of Commons business, to hold the series of votes on different Brexit outcomes.

The amendment has been rejected on previous occasions – at the last time of voting it lost by just two votes – but it has secured at least one new supporter, Tory MP Caroline Spelman, and its backers are now confident of success. Should the amendment pass, May’s meaningful vote could be squeezed into Tuesday.

Subsequent voting options could include the prime minister’s deal, revocation of article 50, a second referendum, a customs union deal, a deal-based single-market model nicknamed “common market 2.0”, a Canada-style agreement, or no deal.

However, Lidington told MPs he did not want to put “unicorn” options to parliament – and in turn was urged to rule out several options including revocation, as well as a Canada-style agreement, which MPs regard as unrealistic.

MPs also insisted May’s deal should not be put to MPs again as an option if it has been defeated for a third time.

Labour’s Stephen Kinnock said it was “vital we only have credible and realistic options on the order paper” and that meant “no options that involve reopening the withdrawal agreement, which is well and truly sealed shut, and no options which are coming out of the blue”.

Lidington is understood to have expressed some caution about letting Speaker John Bercow determine which options are put to MPs, saying he “does sometimes select unicorns”, according to one source.

There is also some disagreement as to whether MPs should vote on ballots for as many options they like, or hold rounds of voting where options are narrowed down – a system that could result in parliament sitting until the early hours of the morning.

Jeremy Corbyn also tabled a less prescriptive amendment calling on the government to set aside time for indicative votes naming four options – Labour’s alternative, common market 2.0, a customs union and a public vote.

The Labour leader, who has held a series of meetings with MPs including those supporting a second referendum and those backing common market 2.0, said he was “convinced that a sensible alternative deal can be agreed by parliament, be negotiated with the EU and bring the public together”.

Ministers conceded on Friday that MPs would probably be given a free vote. Junior Brexit minister Kwasi Kwarteng said it would “be reasonable to have a wide debate in the house to find what the house would tolerate”. Rory Stewart, the prisons minister, said: “Logically speaking, if parliament is to express its view on Wednesday it should be free to express its view.”

Conservative Brexit supporters were seething at the prospect. Steve Baker, one of the key figures in the European Research Group of hard Brexit supporters, said it would be “a national humiliation”. Marcus Fysh, another Tory opponent of May’s deal, said it was “the most ludicrous, childish and unrealistic idea I have ever seen”.

May was facing mounting pressure to name a timetable for her departure as a final gamble to win Conservative votes for her deal, though Tory sources suggested even that option may not have the desired effect.

One moderate Conservative who backed May’s deal predicted the prime minister would be gone within a month. Another MP said the party would “now do almost anything to get rid of her … If Labour called a confidence vote, it would be very interesting”.

The MP for Clacton, Giles Watling, who had backed the deal, said its success “might require the PM to fall on her sword to get it through”.