Theresa May is now thought to be in favour of giving MPs a vote on alternatives to her plans when they debate her Brexit deal.
The prime minister was previously thought to be against this idea.
But sources have told the BBC she wants the "meaningful vote" planned for the third week of January to be a "moment of reckoning" for Brexit.
It comes as the cabinet announced it was stepping up preparations in case there is a no-deal Brexit on 29 March.
The votes would be on amendments to the motion on her Brexit deal - and would take place before the key vote on her plan.
The Brexit deal Theresa May has reached with the EU has to be passed by Parliament but most MPs - including many on her own side - are against it.
She had been planning to present Parliament with a choice between her deal and no-deal, hoping that enough MPs would swallow their objections and get behind her version of Brexit.
But MPs are showing few signs of changing their minds - with some hoping that the next step after her deal being rejected would be leaving without a deal, others hoping for a fresh referendum and some backing alternative deals like the ones Norway or Canada have with the EU.
So rather than wait for what seems like an inevitable defeat, she is thought to be planning a new approach.
The prime minister does not believe any of the factions criticising her plan have enough support to get their own version of Brexit through Parliament.
By allowing them to put forward their proposals and vote on them, she is hoping they will be defeated and her plan will emerge by a process of elimination as the best and only alternative to leaving without a deal.
So what might Mrs May hope to gain?
By BBC Deputy Political Editor John Pienaar
On all sides at Westminster, MPs feel sure her plan is doomed to defeat.
Many - including some in her own Cabinet - want other ideas: a Norway-style Brexit which leaves the UK closely tied to the EU, say, or a referendum, or no deal, put to MPs after that happens.
The prime minister's formula might flush out those who are quietly waiting for her plan to fail before offering their own ideas as a solution.
She wants, in effect, a moment of reckoning for Brexit, with all the rival outcomes debated and voted upon when MPs discuss and decide on her plan next month.
If MPs reject every plan - and that is possible - she might just be able to continue the fight for her own.
Several cabinet ministers have publicly suggested alternative next steps if Mrs May's plan is rejected.
At a marathon cabinet meeting earlier:
- The BBC understands Justice Secretary David Gauke said a "managed no-deal" - which some ministers are thought to favour - is not a viable option. He said it was not on offer from the EU and it was the responsibility of ministers not to propagate unicorns but to slay them
- International Development Secretary Penny Mordaunt, one of those thought to be in favour of a "managed no-deal", is understood to have spoken out against a second referendum
- Sources say Work and Pensions Secretary Amber Rudd, who has advocated a softer, Norway-style Brexit, told the Cabinet "just because you put a seat belt on doesn't mean you should crash the car", adding that a positive future depended on getting a Brexit deal
Mrs May was originally planning to put her plan to a Commons vote last week but pulled it at the last minute over fears it would be defeated, sparking widespread outrage among MPs.
"Last time, for one reason or another, people only set out what they opposed. Next time could be an opportunity for people to set down what they support - and vote on it," a senior source close to Mrs May said.
Downing Street is also hoping to get more reassurances from Brussels that any outcome that keeps the UK tied to EU rules - as part of measures to ensure there is no return to a physical Northern Ireland border, will be temporary.