I ask because this seems to be a very common scenario:
A couple sets out to find someone that they can both be involved with, but then, due to the simple facts of how human relationships form -- which is to say that some die on the vine while some blossom, and it can sometimes take quite a while to discover which it'll be with a given set of people -- one relationship takes root and the other doesn't.
Based on the many personal stories I've read here of people who are either in couples seeking a third partner, or are solo peeps who get involved with both members of a couple, this can lead to a number of problems. These problems seem to be especially bad if those involved, generally the members of the original couple, have strong feelings about a triad being their ideal scenario. If a triad is the goal, then anything else can feel like failure and compounds the natural hurt of rejection.
One issue that seems particularly common is jealousy on the part of the partner with whom it didn't work out. Some of that can seem kindsa childish, along the lines of "she was supposed to be *our* gf and now she's just *your* gf, not fair!!" And some of it is quite understandable... generally, when we break up with someone we want as little to do with them as possible, so that we can have space to heal, but how can you get that space when your ex is still dating your other partner? Especially if, in your idealism over the vision of creating an equal partnership, you moved that new partner in with you all too soon, or in some other way(s) seriously blended your lives. This can be too much for some scorned parties, and they may choose, with heavy hearts, to call the whole thing off... however, once love is on the table, this may not be a viable option anymore. The duo relationship that they started with may have been changed forever and there may be no going back. Or, maybe the partner with whom it was working out DOES agree to call it off... only to find that they can't let go of the resentment that that causes.
The flip side, of course, is that, in order to avoid the above scenario, the newer partner often seems to feel pressure to stay equally involved in both new relationships. As pretty much anyone who's ever dated can tell you, pressure -- the feeling that you need to make this work or else -- is not a healthy thing for a budding relationship.
For all of these reasons, if you're interested in three-person relationships, I tend to advocate framing your search in terms of being open to a triad, not necessarily actively seeking one over other forms of love that may come your way. You're absolutely and entirely right that you can't read the future, but, at the very least, I'd recommend talking to your partner about how you both think you'd try to react in such a scenario.