Theresa May has published a Commons motion that says MPs have considered the next steps in her Brexit plan. The motion will be voted on on 29 January, and MPs have put down a series of amendments.

The government motion is written in neutral terms and is pretty vague: “This house … has considered the written statement” that was tabled by the prime minister this week, which set out the ways she would attempt to find a consensus for her Brexit deal.

Amendments are not legally binding but if any of them get majority support there will be considerable pressure on the government to act according to the will of MPs.

All amendments will be subject to the Speaker’s discretion and it is unclear how many he will allow to proceed to a vote. Here are six of the amendments published so far – and others that could follow.

Extend article 50

Yvette Cooper, the chair of the home affairs select committee, has put down a tightly worded amendment to allow time for a bill that would give parliament the power to support an extension of article 50, which is due to expire on 29 March. Without the amendment, the bill would not be given a slot for debate by MPs.

The bill, devised with the Conservative MP Nick Boles, says that if there is no deal in place before the end of February, the government must put a binding motion before parliament to seek an extension of article 50 until the end of 2019.

A separate amendment has been tabled by Rachel Reeves, the Labour chair of the business select committee, which would directly mandate an extension of article 50, though this amendment would not have the same legal force as that of Cooper and Boles if they manage to pass primary legislation.

Stop no deal

The Labour MP Jack Dromey and the Conservative Caroline Spelman have tabled an amendment ruling out a no-deal Brexit. It is the shortest and simplest of all the amendments tabled so far and does not set out a mechanism for no-deal to be avoided, simply adding to the government’s motion the words “rejects the United Kingdom leaving the EU without a withdrawal agreement and a framework for the future relationship”.

Give parliament more control

The former attorney general Dominic Grieve has put forward a motion to let backbenchers table different Brexit motions for a full day’s debate on six separate days before the UK leaves the EU: 12 and 26 February, and 5, 12, 19 and 26 March. That would give MPs time to debate ideas such as a customs union, Labour’s Brexit plan, a second referendum, no deal and the Norway model. The motions would be amendable and have political force.

Grieve has removed the most controversial aspect of his amendment, seen in one of the leaked drafts, which would have allowed a motion put forward by a minority of 300 MPs from at least five parties – including 10 Tory MPs – to be debated as the first item in the Commons the day after the vote. Instead, the motion now allocates specific days for debate, and the dates have been chosen to avoid any clash with the days specified by Cooper in order to pass her bill.

Grieve has said his amendment is aimed at facilitating a wider debate on the Brexit options. It is similar to a plan for “indicative votes”, floated by several cabinet ministers including the business secretary, Greg Clark, and the education secretary, Damian Hinds.

The six days specified by Grieve could in theory be used to pass primary legislation, but Grieve said that would be difficult and unlikely.

Any bill that required government spending, such as calling a new referendum, would need a “money resolution”, which in turn would need government backing. Grieve told the Guardian he thought that was a constitutional step too far.

A Labour Brexit deal

The Labour frontbench has put down its own amendment that would give parliament a say on a Brexit deal the party could support, including a full customs union, stronger single market alignment and more robust protection for the environment and workers’ rights. It calls for MPs to be given the option of a vote on whether to hold a second referendum.

Limit the Irish backstop

Andrew Murrison, the chair of the Northern Ireland affairs committee, has tabled an amendment to spell out Brexiter demands for a time limit for the Irish backstop. Murrison tabled a similar amendment before the vote on May’s Brexit deal last week, which would have prevented the backstop arrangement from extending beyond 2022, but it was not selected for a vote by the Speaker. His new motion is less specific and says only that the Commons “insists on an expiry date to the backstop”.

Downing Street would probably see such an amendment as useful if it did pass, because it would indicate to Brussels how many MPs could be won over if it did allow a time limit.

A second referendum

The Conservative MP Sarah Wollaston, a leading supporter of the second referendum campaign, has said she intends to put forward a motion calling for a new public vote. However, there is some caution among supporters of a second referendum about the timing. Many believe the idea should only be tested in the Commons when campaigners are sure they can get majority support.

That caution led Wollaston to withdraw an amendment to the prime minister’s Brexit motion last week. It remains to be seen if she can be persuaded to retreat again. The People’s Vote campaign has said its MPs will concentrate on moves to stop a no-deal Brexit and extend article 50.

Indicative votes

Labour’s Hilary Benn, chair of the home affairs select committee, has put down an amendment paving the way for indicative votes on four options recommended by the committee: May’s deal, no deal, a renegotiation based on a Canada or Norway model, and a second referendum.

The independent MP Frank Field, a Brexiter, has drafted a similar amendment, for indicative votes on Brexit deal options that he said could act as a “powerful guide” for the government. His amendment calls for MPs to vote on options including a reformed backstop, no deal, extending article 50, entering into a Canada-style relationship, entering into a Norway-style relationship, a new referendum, and remaining in a customs union.

A citizens’ assembly

The Labour MPs Lisa Nandy and Stella Creasy have been seeking parliamentary support for the idea of forming a citizens’ assembly of voters who could set the direction on the final Brexit deal. Supporters include the Green party MP Caroline Lucas, who has talked to the prime minister about the plan. The MPs could use an amendment to seek parliamentary time to debate the plan next Tuesday.