This comes after the UK Parliament decisively rejected the prime minister’s own deal on two occasions.
The amendment put forward by Oliver Letwin, a lawmaker from May’s Conservatives, changes the rules of parliament on Wednesday, in order to provide time, for indicative votes on Brexit options.
Lawmakers voted by 329 to 302 to accept the amendment. Three ministers resigned from their posts to vote against the government.
They include, British junior foreign minister Alistair Burt and Junior business minister Richard Harrington.
The government issued a statement condemning Parliament’s approval of indicative votes, warning that it sets a “dangerous, unpredictable precedent for the future.”
The government has maintained that it is not bound by the results of the indicative votes.
Lawmakers will now vote on a range of Brexit options on Wednesday, including whether the UK should stay in a customs union with the European Union, and on whether Britain should hold another referendum to decide if it does want to leave after all and then try to push the government in that direction.
Brexit minister Stephen Barclay had said on Sunday that if parliament took control of the Brexit process, a snap election – which the main opposition Labour party would be likely to back – could be the consequence.
May too has made clear that she would not implement a proposal that ran counter to her election manifesto, which promised a clean break with the EU.
Amid the confrontation, the future of Brexit continues to be far from clear.