The proposed changes will be decided upon in the Commons on Wednesday, as politicians wrangle to change Mrs May’s plans.
Voting will take place one-by-one from 7pm, with each expected to take around 15 minutes each.
MPs’ amendments are not legally binding. However if any of them get majority support they add pressure on the government to act on them.
Here are the amendments selected by Speaker John Bercow today:
Amendment A – Labour plan
This is Labour’s proposal, which will seek to force support for the party’s five Brexit demands.
These, it says, would create a Brexit deal the party was able to back.
They are the same as the demands sent by Jeremy Corbyn to Theresa May.
It includes the calls to back a permanent customs union with the EU. The amendment is unlikely to pass.
Amendment K – Rule out no-deal
Tabled by the SNP and Plaid Cymru, this calls upon the Government to rule out any possibility of a no-deal Brexit immediately.
It calls for this to be done “under any and all circumstances”.
It rules that this should be done whenever the time of leaving is.
Amendment C – Bill to extend Article 50
This attempts to ensure an outcome is reached and even allows the Commons to legislate to rule out no-deal.
It was tabled by Conservative Dame Caroline Spelman as well as Labour’s Jack Dromey.
However, it could be revoked should the reassurances on an Article 50 extension vote be forthcoming from the Government.
Amendment B – Treaty on citizens’ rights
Alberto Costa has put this forward in a bid for a treaty with the EU to guarantee citizens’ rights after Brexit.
Mr Costa quit his unpaid role as parliamentary private secretary in the Scotland Office on Wednesday in order to table the amendment.
It seeks guarantees both ways.
Amendment F – Vote on extension
This would look to force Theresa May to stick to commitments she made on Tuesday, namely allowing MPs a chance to vote on delaying Brexit should the PM’s deal not pass.
It was tabled by Yvette Cooper of Labour with the support of Sir Oliver Letwin of the Conservatives.