My opinion on this topic might be a little biased.
I say this because i have been in a 3-way relationship about two years ago back in my junior year of high school. And honestly i didnt think it worked at first because the two were a couple at first and believe it or not it was a str8 couple (why i didnt think it would work). But, they were together for about year before they asked to be in the picture and the three of us lasted 6 months. Could've been longer but the two graduated and went off to college together. And sometimes when their back in town we all get together.
Now i will say its definitely not all gravy its alot that you need to work out (i.e jealous being the biggest one) But like with anyother relationship it takes teamwork you have to trust each other and be willing to work out your issues.