My partner and I work well with an occasional third. Of the very few (probably 3 or 4) long-term trios I know, there is a reason that they work well together. Each one contributes something to the relationship that the other two desire/need but cannot provide. It isn't just 30% more complicated and more work relationship-wise, but probably 300% more.
If it is just a passing fantasy for you, then it should probably stay that way. If it is something that you and your current partner have discussed at length, continue to discuss it, and spend a lot more time on the "downside" aspects than the "upside" ones. Don't pay attention to the nay-sayers who have posted so far and told you that it never works, simply because they don't have the emotional maturity to make something like that work... By the same token, though, don't attempt something like this with a cavalier attitude. A good, healthy "couple" relationship takes a lot of work. A good healthy "trio" relationship takes much much more, but has the potential to offer much much more in return.