If the gridlocked British Parliament had suddenly come to a united Brexit stance on Monday, it would probably have been dismissed as an April Fool’s gag anyway. Of course, no such thing happened.

Monday night’s parliamentary vote saw lawmakers choosing between four Brexit options instead of eight the previous week. Progress of a sort. But once again, they said no to everything.

Partly, that’s down to the process: MPs weren’t told they had to choose just one option, or rank them by order of preference, which would have been revealing.

None of the votes are binding on Theresa May’s government. That meant voting could be used tactically.

If there was any common thread to the results, though, it was that all the options received more votes than May’s deal when it was rejected for a third time on Friday.

This suggests that if there is a consensus somewhere, it’s towards a Brexit that leaves the UK tied more closely to the EU. That isn’t a message to which Brexiteers in May’s ruling Conservative Party are listening.

The option with most support was a “confirmatory” referendum, a public vote to confirm whatever deal Parliament decides on. But even that wouldn’t have moved the ball much.

It would require, firstly, that lawmakers settle on a Brexit path. Then it would need the European Union to grant a long extension to allow for a referendum and the UK to be willing to take part in European Parliament elections in May.

The option closest to a majority, with 276 to 273 votes in favour, was for a permanent customs union with the EU, something already in place as part of Britain’s EU membership.

This would avoid tariffs between the UK and the bloc and would be a relief for British industry, which relies heavily on imported inputs into products that are then exported. It would avoid costly and burdensome rules of origin checks.

A customs union would also go a long way (though not entirely) towards keeping the border open between Northern Ireland and the Republic of Ireland, a problem that has been the chief block on May’s own Brexit deal.

Still, a customs union is far from a “soft” Brexit.

It would entail extra costs and trade frictions, from import/export documentation to regulatory checks for plant and animal products. Nor does it help much with Britain’s all-important services sector, where tariffs don’t apply.

The deal-breaker for Brexit hardliners, however, is that Britain wouldn’t be able to conduct its own trade deals.

This freedom has become totemic for Brexiteers, even if there’s nothing to suggest that the UK would be able to replicate, let alone improve on, the trade terms it already gets around the world as an EU member.

Meanwhile, the clock ticks down to April 12, when Britain will crash out of the EU without a negotiated exit deal unless one of three things happens: Parliament approves a deal; decides to abandon Brexit altogether; or manages to get the EU member states to give it more time. So far, lawmakers can’t agree on a deal and are unwilling to abandon Brexit.

An extension is up to the EU, but the UK would first have to decide what it plans to use it for. Brussels would prefer to avoid a no-deal exit, but patience is wearing thin.

May’s divided Cabinet spent much of yesterday arguing over what to do. Conservatives are deadlocked between several incompatible options: Leaving without a deal; leaving with May’s deal; and pursuing closer ties with the EU through one of the options suggested on Monday. This is tearing the party apart.

Dominic Grieve, the thoughtful former attorney-general and Conservative moderate who has supported a second referendum, faces deselection as an MP by angry local party members.

Nick Boles, the Tory lawmaker whose attempt to build consensus for a Norway-style agreement that would keep Britain in the single market failed on Monday, proclaimed his party incapable of compromise and went to sit as an independent.

Meanwhile, arch-Brexiteers are digging in. One is said to have collected 200 signatures from MPs calling for a “managed” no deal (something the EU says isn’t possible).

Steve Baker, a leading Conservative Eurosceptic, threatened on Monday night to support the opposition in a vote of no-confidence in the Government if May accepted any “softer” option.

It’s getting to the point where it would be braver to just say: Bring it on.

Hardliners like Baker have consistently blocked May’s deal and it is probably time for her to stop pandering and ask a different question, something that should be easier now she’s offered to step down.

That would require her to seek compromise where she can find it, outside of her party. She hasn’t done much of that so far.

There is talk she will offer the opposition Labour Party some kind of assurance that it will play a role in future trade talks with the EU and seek support for her deal on that basis.

The constitutional principle of parliamentary sovereignty, which says that one parliament cannot bind the hands of its successors, makes that tricky.

A different kind of parliamentary voting process, say, using preferential voting, might turn up a more decisive result in future indicative rounds.

Monday’s voting suggests this would probably be a customs union or single market option, both agreeable to Labour, possibly with a confirmatory referendum. But then, it would be up to May to act on it, risking the civil war in her party that she’s been trying to avoid.

In the end, maybe that Tory fracture is simply unavoidable if the country is ever to escape the endless torture of Brexit.

As such, a General Election would at least give voters a chance to choose a new Parliament and perhaps provide fresh impetus for a cross-party solution. It can’t be much worse than the process being held hostage by Baker’s implacable Brexiteers and the Democratic Unionist Party.

There’s a chance, of course, that Brussels may look aghast at an election that could pit Boris Johnson against Labour’s Jeremy Corbyn, and decide to pull the plug anyway by letting the UK leave with no deal.

Indeed, a new class of MPs might not be much better at agreeing a “least bad” path that is bound to disappoint nearly everyone. But they might be humbler and more willing to try.

Therese Raphael writes editorials on European politics and economics for Bloomberg Opinion. She was editorial page editor of The Wall Street Journal Europe