MPs looking to stop no deal are exploring ways to bring back a version of Theresa May’s Brexit deal plus a vote on a second referendum in the last two weeks of October, amid concerns Boris Johnson will still try to pursue a no-deal departure.

Several sources told the Guardian that MPs will spend the next few weeks working on ways to bring back the deal – with added concessions to Labour – to the House of Commons via a backbencher or a temporary prime minister.

MPs working on the options said more Tory and former Tory MPs were now open to backing a Brexit deal with a second referendum added, taking parliament closer to a cross-party majority for the plan.

One former Tory MP said the option was under consideration and would “certainly have to be linked to a referendum”. He added: “We will know in those two weeks whether it is possible or not.”

Another former Tory said: “There is an element of seeing what the next step is from No 10. A lot would be pretty hesitant about backing a referendum until all other options have been tried. But, more attractive, is a way of bringing a deal back on to the table – a version of what was agreed between May and Corbyn. And then have a confirmatory vote attached to it, or someone amends one on.”

Another MP who supports a people’s vote said there were “a number of devices” that could enable MPs to bring forward May’s deal for parliament to work on, and claimed there was “lots of movement in the last 24 to 36 hours” among those trying to stop Johnson ignoring parliament’s direction to request an extension from the EU if a deal is not reached by mid-October.

It comes as Ken Clarke, the veteran Tory who had the whip withdrawn last week, urged Johnson to “put together a cross-party alliance to get a deal through,” as he believed it could now achieve a majority with Labour MPs who regretted having not voted for it previously.

The father of the House told the Byd yn ei Le programme on Welsh-language channel S4C that he would be willing to be an “honorific figurehead” for an alternative government seeking such a compromise if Johnson does not stitch together a deal.

In scathing remarks about the state of politics, he described both Johnson and Jeremy Corbyn as representing “an absurd choice for the premiership of this country” and said the situation was the worst crisis in his political lifetime, amounting to a “tragic farce”.

Theresa May failed to get her Brexit deal through Parliament. Photograph: Mark Duffy/AFP/Getty Images

Parliament has repeatedly failed to find a compromise, but there are signs more opposition MPs are prepared to countenance voting for a deal.

A separate cross-party group of opposition MPs formally launched a campaign to win support for Brexit via a managed deal on Tuesday.

The founders, who include Labour MPs Stephen Kinnock and Caroline Flint, Lib Dem MP Norman Lamb and former Tory MP Rory Stewart – claimed up to 50 MPs may back the plan. Their proposal would involve using elements of Theresa May’s Brexit legislation as the basis for an agreement which Boris Johnson could steer through parliament, possibly in time for a 31 October departure.

Those supporting a second referendum would try to amend any proposal for a deal to secure a “people’s vote”.

Several MPs who support the people’s vote campaign said an increasing number of Tory MPs were coming around to the idea of a confirmatory referendum to break the impasse, including Sir Oliver Letwin, who told the BBC’s Today programme on Tuesday: “If [Boris Johnson] can’t get a deal that he can bring to the House of Commons and get a majority for, there’s another option of course, which is to bring back a deal and ensure a majority for it by attaching it to a referendum.

“I think it’s pretty clear there’s a huge number of Labour MPs, Liberal Democrat MPs, SNP MPs, who would vote for any reasonable deal subject to a referendum and I think there’s now an increasing number of Conservatives and ex-Conservatives who would as well, so I think there is a majority there too.”

The Labour frontbench would be sceptical about voting for any deal that was not negotiated by a Labour prime minister but could come under pressure from many of its MPs and members to compromise if it achieved a second referendum.

Any such moves would increase pressure on Johnson to get his own deal with the EU and on Eurosceptic Tories to back him rather than risk a second referendum.

There is still a possibility that the prime minister could climb down on his demand to entirely replace the backstop with another solution and settle for a more minor tweak to the political declaration, before putting that fresh deal to a vote and challenging the Eurosceptic holdouts to vote for it or lose the whip.

However, he has so far been insistent that what he calls the “antidemocratic backstop” must be removed while the EU is adamant that is not possible, leading to a stalemate on his prospects for a negotiated deal.