After Tuesday night’s crushing defeat for Theresa May’s Brexit deal, there is perhaps one thing on which almost all MPs can agree: there is no obvious consensual route forward. Following are the main possibilities, the obstacles they face and an educated guess at how much support they might command. Most of them would probably involve an extension of article 50 beyond the 29 March deadline. Revoking article 50 is also possible, but unlikely without a second referendum.

Tweaked version of May’s deal

This appears to be the prime minister’s current choice: use the heavy loss to go back to Brussels and beg for another concession on the Irish backstop. The problem is that the only changes to the mechanism that would change minds – a guaranteed end date and/or a unilateral pull-out mechanism – have been definitively ruled out by the EU.

Likely support in Commons: little more than the 202 seen on Tuesday if May secures no real changes.

Quick Guide Brexit and backstops: an explainer Show A backstop is required to ensure there is no hard border in Ireland if a comprehensive free trade deal cannot be signed before the end of 2020. Theresa May has proposed to the EU that the whole of the UK would remain in the customs union after Brexit, but Brussels has said it needs more time to evaluate the proposal. As a result, the EU insists on having its own backstop - the backstop to the backstop - which would mean Northern Ireland would remain in the single market and customs union in the absence of a free trade deal, prompting fierce objections from Conservative hard Brexiters and the DUP, which props up her government. That prompted May to propose a country-wide alternative in which the whole of the UK would remain in parts of the customs union after Brexit. “The EU still requires a ‘backstop to the backstop’ – effectively an insurance policy for the insurance policy. And they want this to be the Northern Ireland-only solution that they had previously proposed,” May told MPs. Raising the stakes, the prime minister said the EU’s insistence amounted to a threat to the constitution of the UK: “We have been clear that we cannot agree to anything that threatens the integrity of our United Kingdom,” she added.

No-deal departure

This is still the default option if MPs find no other way out – a departure on 29 March and a switch to trading on World Trade Organisation terms. However, the Commons has already shown there is a clear majority against this happening, by backing Labour MP Yvette Cooper’s amendment seeking to prevent it happening. And plenty of senior Conservatives have made it clear they would back action to prevent May from pushing ahead with this.

Likely support in Commons: perhaps fewer than 100 would accept it; many fewer want it as a stated ideal choice.

Norway-plus/single market/Efta

These options are closely interlinked, if not the same – for example, the “plus” in Norway-plus refers to the intention of keeping the UK in a customs union as well as a single market, either permanently or until a solution to the Irish border issue can be found. Norway is among the four members of the European Free Trade Association (Efta) – as was the UK before it joined the then-European Economic Community in 1973. Such versions of Brexit would limit economic damage, but require continued freedom of movement for people, which is politically difficult. Also, senior Norwegian politicians have said they would not welcome the UK re-entering Efta.

Likely support in Commons: extremely hard to say. Perhaps around 200, made up mainly of Labour MPs, plus some Conservatives and the Scottish National party. It all depends on the other options on the table.

Quick Guide What is the common market 2.0/Norway-plus Brexit option? Show This soft Brexit compromise has been championed as a plan B for leaving the European Union. It is based on Norway’s relationship with the EU, which is outside the bloc and the customs union but inside the single market. Under the plan the UK would have to join Norway, Liechtenstein and Iceland in the European Free Trade Association (Efta), which would then allow it to participate in the European Economic Area (EEA). The ‘plus’ in this option refers to a temporary customs union with the EU, which would need to be negotiated to avoid a hard border on the island of Ireland. This arrangement would remain in place until the EU and UK agreed a specific trade deal. The option has the advantage of being as close to the EU as possible without full membership, and it would do away with the need for the problematic backstop for Northern Ireland. Like Norway, the UK would be outside the common fisheries and agriculture policies, and would not be subject to the European court of justice. But it crosses a key red line for Brexiters by continuing freedom of movement, one of the preconditions of single market membership. It would also limit the UK's ability to negotiate its own trade deals while a new customs arrangement is under discussion. And it would require continued financial contributions to the EU without an influence, as the UK would no longer have MEPs or a seat on the European Council. It also isn't entirely clear that the UK would be welcomed into Efta.

Customs union

To be precise, “a” customs union, as Labour term it, to distinguish it from “the” existing one based around the EU. Labour, the main proponent of the idea, says it would help businesses with supply chains and solve the Irish border issue. May argues that it goes against the referendum result as it would preclude the UK signing its own trade deals.

Likely support in Commons: most of Labour’s 256 MPs would back this in a whipped vote. Support from others would depend on the rival options on offer.

Second referendum

Otherwise styled as a “people’s vote” by one of the groups advocating it, arguing it would not merely be a repeat referendum but a fresh choice now that the facts of Brexit are known. On the plus side, it would end the deadlock in parliament. Negatives include considerable complexities on timing and vote mechanics, and the bad feeling it could stir in leavers who insist the matter was settled in 2016.

Likely support in Commons: extremely hard to say, anything from 170 to 300, depending on a variety of factors, including whether Labour adopts the plan, and the other options.