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REVOKE ARTICLE 50
The European Court of Justice has ruled that Britain can revoke Article 50 of the Lisbon Treaty - the legal mechanism taking the country out of the EU on 29 March - without the approval of the other 27 member states.
This gives the UK complete control over Brexit, and allows the UK to remain a full member of the European Union if a better deal cannot be struck.
There is some debate over how the government would go about revoking Article 50. And given the divided state of Parliament, it is hard to see how any prime minister could get backing for such a move without a further referendum.
Theresa May has ruled it out because she believes we should stick to the 2016 referendum result regardless of the consequences to the UK. It is not clear if public opinion agrees.
European Council President Donald Tusk has hinted that cancelling Brexit would be his preferred option, tweeting, after Mrs May's deal was defeated by 230 votes: "If a deal is impossible, and no-one wants no deal, then who will finally have the courage to say what the only positive solution is?"
Revoking Article 50 would be the least disruptive alternative as we would continue with our trade arrangements and all of the current EU institutions would be unaffected.
THE QUEEN INTERVENES
With no parliamentary majority for any single course of action - is it time to get the Queen involved?
In Britain's constitutional monarchy, this is not meant to happen. Her Majesty has always remained above the political fray and will, no doubt, want to stay that way. But she is the only person who can invite someone to form a government and become prime minister.
If Theresa May loses a no-confidence vote in the Commons - and Labour has not ruled out tabling more no confidence votes - then this power could come into play.
There would be a 14-day period during which the Queen could ask someone to form a new government if it was clear they could command the confidence of the House. That could be Labour or another Conservative government or a cross-party government.
The Queen would not be able to exercise her own political judgement - everything would depend on whether the would-be new prime minister is deemed to have a realistic chance of getting their laws through Parliament.
One scenario, for the Queen and her advisers, is where it's not clear who has the best chance of winning a confidence vote but different people are making competing claims. If after 14 days, a new government cannot gain MPs' confidence, a general election will follow.
The Queen cannot dissolve Parliament and trigger a general election. The monarch was stripped of that power by the 2011 Fixed-term Parliament Act.
REFERENDUM
A cross-party group of MPs, under the People's Vote banner, is pushing for another EU referendum.
But what would the question be? A direct "Remain or Leave" re-run of the 2016 vote? Leave with a deal or no-deal ? As we do have a deal on the table agreed by both parties No Deal would appear to be contradictory, so a Deal or Remain option would be the most likely choice.
There is a preferred choice voting system that would allow for a 3 question vote.
Vernon Bogdanor, professor of government at King's College, London, has suggested the Brexit impasse could be resolved by holding two further referendums, a few weeks apart - the first, a straight Leave or Remain choice. Then, if Leave won, another vote on the terms of departure.
