Jeremy Corbyn was considering throwing Labour’s weight behind a “common market 2.0” soft Brexit deal as MPs considered which options to back in indicative votes on Wednesday.

MPs voted on Monday to seize control of the parliamentary timetable to allow the House of Commons to explore whether there could be support for alternatives to Theresa May’s twice-defeated deal.

Labour frontbenchers held a wide-ranging discussion at a weekly shadow cabinet meeting on Tuesday about how to manage the complex process and whether the party’s MPs should be given a free vote.

They broke up with no firm decision having been made, although one shadow minister said: There was a clear sense that we will whip along the lines of what our party policy is.”

MPs will be offered a series of options on a paper ballot and given the opportunity to choose as many as they want to support, in the hope it will become clearer whether any alternative to the prime minister’s agreement could command a majority.

Another set of votes is likely to be held next Monday to continue the process of whittling down options, though it is probable May will have another go at winning a majority for her deal in the interim.

Labour tabled its own Brexit policy on Tuesday night as one of the options to be considered by MPs. The motion reflected the wording in Corbyn’s recent letter to the prime minister calling for a customs union and single market alignment.

In a statement accompanying the motion, Corbyn said: “The government’s approach to the Brexit negotiations has been an abject failure and this house must now come together to find a way forward. Labour’s credible alternative plan can be negotiated with the EU and bring people together, whether they voted leave or remain.”

However, the party is also considering whether it can support a separate motion tabled by the Labour MPs Stephen Kinnock and Lucy Powell, and signed by several Tories, including Robert Halfon and Nick Boles.

Kinnock and Powell are part of a cross-party group that has been working for months on proposals for a Norway-style arrangement after Brexit, involving membership of the European Free Trade Association.

This soft-Brexit alternative would keep the UK in the single market by remaining in the European Economic Area and Efta.

Corbyn has held a series of meetings with the MPs proposing such a departure in recent weeks, and the Guardian understands key members of the Labour leader’s team have discussed the drafting of the policy, which is aimed at winning support from members of all parties.

Kinnock said: “Labour’s frontbench motion calls for single market alignment and shared institutions. “Common market 2.0” simply puts flesh on the bones of that motion, by committing to full participation in the single market through membership of the European Economic Area.

“Our cross-party group of MPs has had very constructive and positive discussions with Jeremy, Keir [Starmer] and John [McDonnell].”

However, supporting any version of Brexit will be anathema to Labour MPs campaigning for a fresh referendum in the hope of revoking article 50 and remaining in the EU. And some Labour MPs from leave-voting constituencies are likely to have worries about the lack of control over immigration.

There were also concerns as to whether Labour could trust May, or any potential successor, to implement a softer Brexit if that is what parliament decides.

“If we can get a majority for May’s withdrawal agreement plus a customs union, the risk is that either this prime minister won’t deliver it, or you vote for it, write that into a political declaration and that is handed to a new Tory prime minister like Boris Johnson who can just rip it up,” one shadow cabinet minister said. “It will come down to a very difficult call for the party.”

Tensions in Labour over Brexit have abated somewhat in recent weeks after some of the fiercest critics of the leadership’s stance left to join the breakaway Independent Group.

Corbyn and the shadow Brexit secretary, Keir Starmer, subsequently announced Labour would support a pro-referendum amendment earlier this month.

But Corbyn’s decision to skip the anti-Brexit march on Saturday, while frontbenchers including Clive Lewis and Tom Watson attended, underlined the divisions in the party.

Supporters of a people’s vote decided to table a motion calling for a referendum as one Brexit option on Tuesday night, after an intense discussion over tactics. Some had earlier suggested the moment to press the issue was after parliament had chosen a deal to support.

One leading supporter of the People’s Vote campaign said they would vote for “referendum or revoke, nothing else”. Labour was expected to encourage its MPs to support the motion, though no final decision had been taken.

Some of those backing a referendum said it was the wrong tactic to table the option now. The Conservative former minister Justine Greening said: “Indicative votes are about what substantive route forward we have on Brexit. That is distinct from the question about having a confirmatory public vote on whatever parliament decides.”