There was a major row in the Commons over whether the amendment could even be put to a vote, with Speaker John Bercow apparently disregarding the advice of his own clerks that it could not.
On Wednesday, Parliament voted for an amendment calling on the government to set out its Plan B within three working parliamentary days of the January 15 vote, rather than the 21 days specified in Brexit law.
MPs have voted to further bind Theresa May's hands on Brexit - if she loses her deal next week - by 308 to 297.
The news comes the same week the government suffered two humiliating defeats in the Commons.
He also argued that Theresa May is struggling badly to get a deal agreed because "the Prime Minister and the government have pushed parliament away" to secure any form of consensus. Current rules dictate that Mrs May would have to make a statement within 21 days on the Government's plan of action, with a Commons vote in the following seven days.
But opposition remains strong from both pro-Brexit and pro-EU U.K. lawmakers.
Mr Bercow admitted there was no precedent for his decision, but told MPs that centuries of convention did not "completely bind" him.
A majority of members of Parliament oppose a no-deal Brexit, but it remains the default option if May's deal is rejected.
May has refused to retreat from her unpopular deal, which envisages close trading ties with the European Union after leaving in March.
May called off a vote on her deal in December after admitting that it "would be rejected by a significant margin" if MPs voted on it.
Groups of MPs have raised several options, including a Norway-style arrangement that would see Britain remain outside EU institutions, such as the European Court of Justice, but within the European single market, which provides for the free movement of goods, services and people.
This will take the form of a motion she lays before the Commons.
In a speech on Thursday, Mr Corbyn will say that Mrs May - who abandoned a vote on the deal last month - will forfeit the right to govern if she can not get her Brexit deal through the Commons.
Many Brexiter MPs were furious with Bercow, believing it was effectively unconstitutional to allow a business motion - which sets out what MPs are about to debate and vote on - to be amended. Sammy Wilson, the party's Brexit spokesman, said: "The only thing which could swing the DUP round is if the backstop as it applies to the United Kingdom as a whole or to Northern Ireland specifically were removed from this agreement".
The amendment was passed, much to the discomfiture of the ruling benches. May's deal or remaining in the EU.
"The only way we can move forward if the Government's deal is not acceptable to Parliament is for Parliament to engage with Government and find a solution, which is what I am trying to do".
"This is a time for parliament to come together and work intensively to establish an agreement that can command majority support".
He will say: "A government that can not get its business through the House of Commons is no government at all".
"If the government can not pass its most important legislation, then there must be a general election at the earliest opportunity", Labour leader Jeremy Corbyn will say, according to the text of a speech he will deliver in Wakefield, northern England, extracts of which were released by Labour.