I have to say I'm not convinced by BSs assertion that the British Prime Minister (Taoiseach) is a Brexiteer... but, if she is, that's how it ought to play out. With cross party support the deal would be approved. At this stage it may require a short delay to reposition some periods and commas so the leader of the opposition can claim some input.
However, I reckon the British Prime Minister (Taoiseach) and the civil service want to remain. Hence I suspect they want the deal defeated a third time having informed the house that such a defeat will require a long extension and also require Britain to participate in the European elections. Bearing in mind that she has already told the house that any new referendum will include a remain option, from there on the choreography will switch to remain.