It would also be legally very difficult to have a muilple choice referendum any more than a binary choice has problems with the maths and legality the so called people's vote which the small number of hard core remainer politicians want is probably not possible they would have to re-run the referendum again which would be crazy. By the way leave would win again by a mile
You can also just have 2 rounds as some do it for presidential elections. Otherwise how do you go about with the parliament not getting a majority, just crash out?
We can't change our constitution to suit a few remainers. A multiple choice referendum there is some debate whether it would be legal. Say there are four options 26% of the voters could win politically it would be a farce. It's also prone to being influenced by action groups given there would be a very low turnout. It would be a farce. The only option would be another in or out referendum because they didn't accept the first answer again completely crazy. Plus either option would take years referendums have to be done strictly to parliament law. Thinking about it today there are only three options
1- we agree a deal that respects the referendum and works for the EU and UK.
2- we go onto WTO
3- we do a straightforward Canada type deal.
I don't believe any other option is possible. There is talk of a chequers minus minus deal however parliament (100 brexit Tory MP,s) would reject that plus the Tories would not be elected ever again. So that's out another referendum is out so that leaves only those three. As for the Irish border well they have allowed it to be a pawn of the EU and hence they will have to take what comes.