THE debate over Brexit is becoming feverish. The past week has seen reports of cabinet splits; of the European Council’s president saying, just before Theresa May’s first EU summit, that the only choice is between a hard Brexit and no Brexit; and of the government’s plan to allow Parliament a vote on the eventual terms of a deal. All this comes before formal negotiations have even begun. One observer says the government is behaving as if it is negotiating with itself, not with 27 other countries and the EU institutions.

One example is the issue of whether, if Britain quit the EU’s single market, it could secure special access for key industries. The City of London wants a deal for financial services, and there is talk of paying into the EU budget to secure one. Mrs May has assured Nissan, whose Sunderland car plant is the biggest in Britain, that it will not lose from Brexit; at least one other carmaker has had a similar pledge, and others will no doubt ask too. Universities have suggested that students might be exempt from visas for EU migrants.

How plausible are sectoral deals? In principle, the EU can agree to anything. Norway is in the single market (but not the customs union) via the European Economic Area. Switzerland is not, but it has bilateral deals, including one giving it full access for non-life insurance. John Springford at the Centre for European Reform, a think-tank, says it would be technically possible for the British car industry to remain in the EU’s customs union. Malcolm Harbour, a former Tory MEP who chaired the European Parliament’s internal market committee, suggests the entire transport sector might stay in the single market.

Yet there would be a price to pay. Mujtaba Rahman of the Eurasia group, a consultancy, says the other 27 EU countries are clearer than ever on the indivisibility of the single market’s “four freedoms” of movement of goods, services, capital and labour, which apply also to Norway and Switzerland. Any sectoral deal would be policed by the European Commission and the European Court of Justice. Yet Mrs May has ruled out unfettered free movement of people and the jurisdiction of the court. As for continuing budget payments, an idea she has not dismissed, Mr Rahman says they might improve the mood, but not enough to secure special deals that override the four freedoms.

The politics of sectoral deals could be even worse. The other 27 countries insist that Britain should not be better off than it was as an EU member, and they are united in opposing cherry-picking. Yet that is exactly what sectoral deals would do. If the British win special treatment for finance and cars, why not the Dutch for tulips and windmills, the French for cheese and cosmetics, the Germans for machine tools and engines—or the Poles for fruit-pickers and builders? Were all countries to get special privileges for their favoured industries, warns Neil Carmichael, a pro-EU Tory MP, the single market could collapse into a mess of protection and subsidies.

World Trade Organisation (WTO) rules would also make sectoral post-Brexit deals harder. If Britain were to agree bilaterally with the EU not to apply tariffs on cars, the WTO’s “most favoured nation” principle might force it to offer tariff-free access to the rest of the world as well. The only way to avoid this would be a full-blown free-trade agreement, which is by definition not sectoral but covers most trade.

Mrs May’s eventual choices will boil down to three. First is an option like Norway’s that secures largely barrier-free access to the single market but involves customs controls and accepting EU laws, migrants and budget payments. Second is a free-trade agreement that avoids such obligations but excludes most services and would take years to negotiate and ratify. And third is trading on plain WTO terms, which implies tariffs on cars and other products and also excludes services. The Treasury’s central estimate is that this option would lower GDP by 7.5% after 15 years. No wonder the Brexit debate is so febrile.