The government is reportedly discussing plans to stage seven "indicative votes" next week on what to do if it again rejects the prime minister's Brexit deal.
These are set to include the options of holding a second referendum, adopting a softer Brexit, or simply revoking the Article 50 process through which Britain is set to leave the EU.
Asked about the plan on Friday, Conservative Brexit minister Kwasi Kwarteng indicated that the votes would be "free" with the government not instructing their MPs how to vote.
"Obviously if the House is being asked to find a way forward it would be surprising if those votes were not free votes," Kwarteng told the House of Commons.
May's deputy David Lidington signalled last week that MPs would have further chances to express their views on Brexit.
Lidington is also reportedly considering holding a series of "run-off" votes if none of the offered alternatives wins a majority in Parliament.
While the government has not yet officially committed to holding indicative votes on Brexit, an amendment set to be brought forward by Conservative MP Oliver Letwin on Monday could force ministers to do so, if it is endorsed by a majority of MPs.
The reported plan has led to a furious reaction from Conservative Brexiteers.
"National humiliation is imminent through these 'indicative votes,'" said European Research Group spokesman and former Brexit minister, Steve Baker.
He added: "The wrong Conservatives have the levers of power."
Conservative MP Michael Fabricant tweeted "If this is true, has Theresa May now decided to declare open war on ALL her backbenchers following her ill-advised statement last Wednesday night?"
His colleague Marcus Fysh described the proposal as "the most ludicrous, childish and unrealistic idea I have ever seen."
