MPs will have their say on them this evening ahead of deciding whether Theresa May should be given authority to request an Article 50 extension from the EU.
This comes after MPs voted yesterday in favour of ruling out a no deal Brexit, with a majority not backing such an outcome whatever the circumstances.
The amendments look to shape the next step of the Brexit saga in a number of ways from allowing a cross-party group of MPs to take control of the process to even touting the prospect of a second referendum.
An amendment which was aimed at ruling out a second referendum, or "people's vote", was not selected by Mr Bercow sparking anger from some Brexiteers.
The Standard gives further details of the four chosen amendments below:
Amendment H - Second referendum
This seeks an Article 50 extension to stage a second referendum.
The vote would have Remain and Parliament's preferred Brexit option on the ballot paper.
It was tabled by Independent Group MP Sarah Wollaston and backed by members of the new grouping of Tory and Labour defectors.
The Liberal Democrats and a handful from other parties also back the idea.
Mrs May has long rejected calls for such a vote, stating her desire to "fulfil" Brexit following the referendum.
Amendment I - MPs take control
This would seek to allow MPs in the Commons to take control of the Brexit process.
It has been tabled by Conservative MP Sir Oliver Letwin, Labour's Hilary Benn and Yvette Cooper.
It aims to "enable the House of Commons to find a way forward that can command majority support".
It would dictate that on Wednesday March 20 the standing order stating that Government business has precedence would not apply.
Instead, precedence would go to a motion in the name of 25 MPs "relating to the Business of the House on a future day or days in connection with matters relating to the United Kingdom's withdrawal from the European Union".
The amendment also bears the names of Dominic Grieve, Norman Lamb, Stewart Hosie and Ben Lake.
Amendment E - Time to find a new approach
This amendment from Labour states Parliament has "decisively" rejected both Mrs May's deal and no deal.
It then calls for a delay to Brexit "to provide parliamentary time for this House to find a majority for a different approach".
Labour leader Jeremy Corbyn has frequently spoken of his party’s potential plans which he feels could be agreed with the EU and get a majority of support in the Commons.
His plans would involve some form of customs union with the EU, which Mrs May and he have clashed over.
Amendment J - No third meaningful vote on May's deal
This amendment has been motioned by Labour MP Chris Bryant.
It calls for the Speaker to be given the power to block a third meaningful vote on the PM's Brexit deal.
This has already been the subject of two major defeats in the Commons.
Following the vote on Thursday it is set at present for Mrs May's deal to be voted on by Parliament once again next week.
The embattled PM has frequently touted that her deal is the best available, with the EU also not budging on there being a different plan on offer.