LONDON (Reuters) - Prime Minister Theresa May has proposed a collaborative approach to finding a new Brexit deal after the agreement she had negotiated was crushed by parliament on Tuesday in the biggest defeat for a British government in modern times.

FILE PHOTO: Britain's Prime Minister Theresa May leaves Downing Street, as she faces a no confidence vote after Parliament rejected her Brexit deal, in London, Britain, January 16, 2019. REUTERS/Clodagh Kilcoyne

What is her new approach, and will it work?

WHAT IS MAY PROPOSING?

Immediately after Tuesday’s 432 to 202 defeat, May said she would meet with senior parliamentarians from all parties to seek a deal that could command the support of parliament and was “genuinely negotiable”. She said there was an urgent need to make progress.

She has sought meetings with the leaders of all other opposition parties in parliament and committed to make a statement on her new approach on Jan. 21.

WILL IT WORK?

May is largely keeping to the negotiating principles she has used throughout the Brexit talks, which have alienated different factions of lawmakers on different points.

There is no single policy change May can make that both respects her negotiating principles and can win over enough lawmakers to get parliamentary approval.

Any change she makes to appeal to one group will probably cost her votes from another faction.

WHAT IS UP FOR DISCUSSION?

May has set out the terms on which she is willing to talk. She refers to them as principles for the discussion, others call them “red lines”. These are the key issues:

- 1. NO-DEAL BREXIT

May’s preference is to leave the EU with a deal, but she does not rule out leaving without a deal.

If May said she wanted to leave without a deal she would gain the support of some Conservative euroskeptics, but lose the support of pro-EU lawmakers in her party and rule out winning votes from almost all opposition parties.

If she ruled out leaving without a deal, she would open up the possibility of gaining votes from the opposition Labour party and pro-EU Conservative lawmakers, but would alienate Conservative Brexit supporters who say the threat of such a departure is a crucial bargaining chip in talks with the EU.

- 2. DELAY BREXIT

May wants Britain to leave on March 29, the date set down in British law.

If she chose to try to delay that date she would lose the support of Conservative euroskeptics, but open up the possibility of winning votes from other parties. However, on its own, this would not be enough to win opponents’ support.

- 3. THE BACKSTOP

May has agreed to an insurance policy designed to prevent the return of border posts and checks on the frontier between EU-member Ireland and Northern Ireland, and so ensure respect for a pact that has secured more than 20 years of inter-communal peace in the once-troubled British province.

This has cost her the votes of Northern Ireland’s Democratic Unionist Party, which props up her minority government, and a large cohort of euroskeptic lawmakers in her own party.

If she successfully removed or altered the so-called ‘backstop’ she could win the support of many critics in her own party and bring the DUP on board.

But the European Union, defending Ireland’s interests, has insisted there cannot be a deal without the backstop.

- 4. END FREE MOVEMENT

May says any deal must give Britain control of its borders, laws, and money. This refers to an ambition to end free movement of people from the EU, end the jurisdiction of the European Court of Justice and stop making membership payments to the EU.

By dropping the requirement to end free movement, May would open up the possibility of a ‘softer’ Brexit that involves remaining a member of the EU single market, for instance one modeled on Norway’s relationship with the EU.

This could win the support of pro-EU lawmakers in her own party, and could help to win over some opposition members of parliament. But it would cost her the votes of Conservative euroskeptics, who argue it would not be a “true Brexit”.

- 5. INDEPENDENT TRADE POLICY

May insists that Britain must be free to strike free trade deals with other countries. This effectively rules out Britain remaining in the EU customs union, or setting up a new permanent customs union with the EU.

Changing this policy would meet one of the main demands of the opposition Labour Party, but would cost May the votes of Conservative euroskeptics and some others who say it would tie Britain into a set of rules that it had little power to influence.