All the options were defeated. The U.K. now faces a deadline of April 12 to present the EU with a new Brexit plan or crash out of the bloc that night. British lawmakers plan another round of votes Monday to see whether they can come to an agreement on a way for Britain to leave the bloc. And May hasn't given up hope of persuading Parliament to back her Brexit deal if she asks a fourth time.
A look at the most likely options:
EU CUSTOMS UNION
The option that came closest to success in last week's "indicative votes" in Parliament called for Britain to remain in a customs union with the EU after it leaves.
May has always ruled that out, because sticking to EU trade rules would limit Britain's ability to forge new trade deals around the world.
But it would ensure U.K. businesses can continue to trade with the EU, and would solve many of the problems that bedevil May's deal. In particular, it would remove the need for customs posts and border checks between Ireland and Northern Ireland.
The option has been put forward again for a vote on Monday, alongside variations including remaining in the customs union and the EU's single market for goods and services, and staying in the single market but not the customs union. It's a confused picture not guaranteed to produce a majority for anything.
But if a customs union pledge was agreed by Parliament, it would likely be welcomed by the EU and would allow Britain to leave the bloc in an orderly fashion in the next few months.
May, however, is under pressure from pro-Brexit members of her government not to tack toward a softer Brexit.
NEW BREXIT REFERENDUM
Another option with significant support is for any Brexit deal to be put to public vote in a "confirmatory referendum." The idea came within 27 votes of winning last week, and is backed by opposition parties, plus some of May's Conservatives.
Her government has ruled out holding another referendum on Britain's EU membership, saying voters made their decision to leave the bloc in 2016.
But with Parliament and May's Cabinet divided, a new plebiscite could be seen as the only way to move forward.
Parliament has voted repeatedly to rule out a no-deal Brexit — but that remains the default position unless a deal is approved, Brexit is canceled or the EU grants Britain another extension.
Most politicians, economists and business groups think leaving the world's largest trading bloc without an agreement would be disastrous. It would impose tariffs on trade between Britain and the EU, bring customs checks that could cause gridlock at ports, and might spark shortages of essential goods.
Brexiteer lawmakers in Britain's governing Conservative Party dismiss this as "Project Fear" and argue for what they call a "clean Brexit." They have urged May not to compromise and to ramp up preparations to leave the bloc without an agreement on April 12.
May has said repeatedly she does not believe Parliament would allow a no-deal Brexit to happen.
LONG DELAY OR NO EXIT
The alternative to a "no-deal" departure is to delay Brexit for at least several months, and possibly more than a year, while Britain sorts out the mess. The EU is frustrated with the impasse, and has said it will only grant another postponement if Britain comes up with a whole new Brexit plan.
The bloc is reluctant to have a departing Britain participate in the May 23-26 European parliament elections, but that would have to be done if Brexit is delayed. Still, EU Council President Donald Tusk has urged the bloc to give Britain a Brexit extension if it plans to change course.
A long delay raises the chances of an early British election, which could rearrange Parliament and break the political deadlock. It also keeps alive the possibility that Britain does not leave the bloc.
MAY'S BREXIT DEAL
After almost two years of negotiations, Britain and the EU struck a divorce deal in November, laying out the terms of Britain's departure from the bloc and giving a rough outline of future relations.
But it has been roundly rejected by lawmakers on both sides of Britain's Brexit divide. Pro-Brexit lawmakers think it keeps Britain too closely tied to EU rules. Pro-EU legislators argue it is worse than the U.K.'s current status as an EU member.
Parliament has thrown it out three times, although the latest defeat, by 58 votes, was the narrowest yet. It was rejected even after May won over some pro-Brexit lawmakers by promising to quit if it was approved.
May is considering one last push, pitting her deal against whatever is agreed upon by Parliament, in hopes that hold-out Brexiteers would back her deal rather than a softer option.
Follow AP's full coverage of Brexit at: https://www.apnews.com/Brexit