At that point you're basically discussion voting systems. Using first-past-the-post with three options, two of them being breixt, would heavily rig the vote towards remain.

Improving voting systems would be great (especially looking at the US, if you ever want more than two real parties), but doing it on the back of such an important decision would be problematic at best.

Here is a cutesy video for those new to FPTP voting issues: https://youtu.be/s7tWHJfhiyo