MPs have voted to take control of Commons business in an unprecedented move to try to find a majority for any Brexit option.
The government was defeated by 329 votes to 302 on the cross-party amendment setting up a series of votes on Wednesday to find out what kind of Brexit has most support among MPs.
PM Theresa May has said there is no guarantee she will abide by their wish.
Thirty Tory MPs voted against the government, including three ministers.
Richard Harrington, Alistair Burt and Steve Brine resigned to join the rebels, with Mr Harrington accusing the government of “playing roulette with the lives and livelihoods” of Britons.
Mr Harrington said in his resignation letter that as industry minister, he had been told the government approach was “resulting in cancelled investment decisions, business being placed abroad, and a sense of ridicule for British businesses”.