Why wouldn't 3 options work on a referendum? Wikipedia's section on multiple choice referendums[0] shows that they have been run in other places in the past, using methods such as the ranked-voting Single Transferable Vote method.

Being able to rank the option would thwart claims of trying to split either side of the vote, if e.g. leavers could rank all the leave options above all remain options.

[0] Interestingly, not "referenda": https://en.wikipedia.org/wiki/Referendum#Etymology_and_plural_form