I found an article in the 21st July edition of The Economist quite intriguing. It analysed the results of a YouGov poll in June 2018 which actually did a 3-way poll on preferences for Remain, Soft Brexit, Hard Brexit (as suggested in June by MP Justine Greening). The intriguing part was that several voting systems were used.
First past the post: 1. Remain 40, 2. Hard 37, 3. Soft 14
Shows the country deeply divided. Few people profess to want the soft Brexit being pursued by Theresa May.
Alternative Vote: 1. Hard 47, 2. Remain 44
When the 14% soft votes are apportioned according to second preferences, the result is reversed and Hard wins. Of course, this pretty well reflects the result of the 2016 referendum.
Comparisons (Condorcet Method): Soft beats Remain, Soft beats Hard, Hard beats Remain
When people are asked to compare the options, two at a time, Soft comes out as the winner. So deep down this suggests that the soft Brexit being pursued by Mrs May is the compromise that in the end satisfies most people.
Beware voting system!
Although plausible, a three-way referendum could actually be rather problematic and totally dependent on the voting system used, let alone the interference effects of Big Money and Russian Bots!