After John Bercow ruled on Monday that there would not be another vote on Theresa May’s Brexit deal if it was “the same proposition or substantially the same proposition”, the immediate prospects for ‘Meaningful Vote 3’ seemed to recede.

But even if May is able to set out a new version of the deal that is distinct enough to secure the Speaker’s approval, and then wins the backing of the Democratic Unionist Party, the prime minister faces yet another major barrier to getting her plan through the Commons: the European Research Group.

Chaired by Jacob Rees-Mogg, the ERG brings together many strongly pro-Brexit Conservative MPs, the great majority of whom have, so far, voted against her deal.

The ERG does not publish membership records, but a letter to May last year from the group about her Brexit plans was signed by 62 Conservative MPs.

However, the ERG is not a homogenous bunch, and not all Conservative Brexiters are members. Here is a guide to the broad tribes within it, and how they might lean if there were to be a third vote on the PM’s Brexit plan.

The irreconcilables

These are the diehards, for whom May’s warnings that a failure to support her deal could mean a long-delayed Brexit, or even no Brexit, ring hollow. These are the ideological leavers, prominent among them Mark Francois, Steve Baker, Andrea Jenkyns and former Brexit minister David Jones.

They were all among 23 signatories to a letter in Monday’s Telegraph querying the stated choice between backing May’s plan and a long delay, saying it would be wrong to “cast a positive vote in favour of either for fear of the other”.

The long-term leavers

A group that often crosses over with the irreconcilables – for example John Redwood – but is distinguished in the main by the sheer extent of time these MPs have been arguing the Brexit cause. Others who can be put in this category include Bernard Jenkin, Iain Duncan Smith and Christopher Chope. Not all are ERG members – for example, passionate leaver Peter Bone stresses he is not part of the caucus.

The reluctant converts

These are the people May is banking on to get her deal through parliament: MPs who voted against it twice, still don’t especially like it, but have decided it is probably the least bad option. The most prominent so far has been the former work and pensions secretary Esther McVey, who said the removal of no deal as an option meant things had changed. Other switchers include Daniel Kawczynski and Philip Davies.

The waverers

Another key group. Chief among them is none other than Rees-Mogg, who said on Monday he was awaiting the verdict of the DUP before making up his mind. “No deal is better than a bad deal, but a bad deal is better than remaining in the Europe Union,” he told LBC radio. If Rees-Mogg – a two-time Commons opponent of May’s plan – changes his mind, then others would be expected to follow. It’s hard to tell who that will be, but they are likely to be among ERG members who did not sign Monday’s Telegraph letter, such as Iain Duncan Smith and Desmond Swayne.

The careerists

Another contingent whose Venn-diagram set crosses over with several others, comprising current or former ERG supporters whose decisions on May’s deal have to be seen through the prism of their leadership ambitions. Chief among these, of course, is Boris Johnson, who devoted his weekly Telegraph column on Monday to explaining why he cannot support the plan.

Similarly, the former Brexit secretary Dominic Raab is already manoeuvring for a post-May bid, and seems minded to oppose the deal again. On the other side of the vote divide, McVey has also indicated she could stand.