The Labour leadership this month drafted its own amendment to replace the Lords' one on the EEA, demanding a vote on negotiating a new single market deal with the bloc. This won the support of the Commons by 325 votes to 298. That has potentially seismic consequences for the protracted and increasingly messy split from Brussels.
The government on Thursday published detailed plans for a so-called "temporary customs arrangement" with the EU.
"There are people in this palace, your palace, who are attempting to do everything in their power to overturn that decision and to create a meaningless, toothless, neutered Brexit".
Hours before the debate began, a justice minister resigned in protest at what he called its "wish to limit" the role of parliament in shaping Brexit.
We urgently need legal certainty about post-Brexit arrangements in Ireland for our political and economic stability. The Lords themselves would get chance to consider a motion, but that wouldn't mean a binding "yes" or "no" vote for them.
Yesterday May agreed in principle to give MPs significant powers to shape the Brexit process.
Pro-EU Tories have warned that they remain ready to rebel if their demands are not satisfied by the compromise amendment, before leading Brexiteer Jacob Rees-Mogg claimed their idea made a "no-deal Brexit" more likely. Opening the debate, Brexit Secretary David Davis said: "What it actually amounts to is an unconstitutional shift, which risks undermining our negotiations with the European Union".
Public policy expert Richard Bull of Pinsent Masons, the law firm behind Out-Law.com, said, however, that the MPs would have another opportunity to defeat the government if the promised concessions did not materialise.
The parliamentary votes on June 13 were less dramatic.More news: E3 2018: Beyond Good And Evil 2 Gets New Trailers
It was Labour divisions that were exposed on Wednesday by votes on the EEA plan.
"And my constituents, those Leave constituents, who have been insulted, day in, day out, by some of the comments in this House are not against all migration, but they do want to have a sense that we can turn the tap on and off when we choose".
Potential Tory rebels held back from a threatened revolt on Tuesday after a face-to-face meeting in which the Prime Minister was said to have offer "personal assurances" on concessions.
May also pledged, the rebels said, to consider the third section of the amendment, which would prevent a no deal Brexit by putting Parliament in charge if no agreement is reached with the European Union by 15 February next year.
"If we are heading for an impasse in November, everything is on the table". The upper chamber, the House of Lords, inserted amendments in 15 areas to soften the departure.
The Bracknell MP, who called for a second referendum on whatever deal Mrs May secures from the European Union, later told the Commons there was growing evidence that the Government's Brexit policy is "detrimental to the people we were elected to serve".
Another Conservative Remainer, former Cabinet minister Nicky Morgan, denied that the rebels had been "played" by the Prime Minister.
One government official said: "It's not over yet". Then her foreign minister, Boris Johnson, was recorded saying there could be a Brexit meltdown.
Keir Starmer, Labour's shadow Brexit secretary, was refusing to accept the government at its word Tuesday.