The parliamentary notion covers both a scenario under which Prime Minister Theresa May breaks the deadlock at home and manages to get the divorce deal she had negotiated with the European Union ratified in the UK Parliament, as well as a no-deal Brexit.
A number of Kent Conservative MPs who had helped sabotage the original deal put to the Commons a fortnight ago swung behind an amendment that removed the Northern Ireland backstop and replaced it with "alternative arrangements" - although what these are is unclear.
European Union officials have been adamant for months, however, that there is no room to renegotiate the so-called "backstop" element of the current draft Brexit plan, which is created to keep the Ireland-Northern Ireland border open regardless of whether a final customs deal is reached.
Another amendment, rejecting a no-deal Brexit, also won the support of Parliament yesterday.
The intervention comes ahead of a crucial day for May's Brexit deal on Tuesday, with Parliament considering a number of amendments that could prevent Britain from leaving the European Union without an agreement on future relations.
Earlier this month, the deal was overwhelmingly rejected by the Commons.
May believes her agreement can still win Parliament's backing if it is changed to alleviate concerns about the Irish border measure, known as the backstop.
Instead, the Cooper-Boles plan could now win more backing from politicians who are determined to stop a no-deal Brexit and ensure they have the power to delay the UK's divorce from the European Union if necessary.
She vowed to go to Brussels and seek "significant and legally binding change" to the backstop.
Prime Minister Theresa May addressing the House of Commons.
Sabine Weyand, deputy to EU Brexit negotiator Michel Barnier, said: "There's no negotiation between the EU and the UK".
Sterling is plunging against the U.S. dollar (GBPUSD=X) after a certain major amendment to prime minister Theresa May's Brexit deal was voted down.
She said the government will come back to make a statement to Parliament on the next steps if no Brexit deal has been agreed by February 13.
European Commission vice-president Jyrki Kateinen said there was "no reason to give any concessions" to the United Kingdom and there was "not much room for manoeuvre" on the backstop.
Mr Lewis confirmed that the Government would whip against an amendment co-sponsored by one of its own MPs, Nick Boles, which seeks to extend the Article 50 period to avoid a no-deal Brexit.
The prime minister's spokesman said Mrs May would "engage" with her colleagues to discuss the plan, but she would also be looking at a possible time limit or a unilateral exit clause to the backstop as other "alternatives".
She said it was a chance to, "tell Brussels that the current nature of the backstop is the key reason Parliament can not support this deal".
And Ireland's European Affairs Minister, Helen McEntee, cautioned: "There can be no change to the backstop".
Another would let lawmakers vote on a set of alternate Brexit proposals to see which - if any - could muster majority support.
Markets have bid Sterling up over recent days on the view that Cooper's amendment is an insurance policy against a "no deal" Brexit taking place, based on the assumption there is a parliamentary majority against a "no deal" Brexit. "We have the vote tonight and then we will take it from there", he said.
Leave supporting MPs have accused the speaker, who publicly declared that he voted for Remain, of using his position, which is traditionally impartial, to try to scupper Brexit, and will be keeping a close eye on his actions on Tuesday.