Doesn’t really exist, does it? Due to the romantic systems in place, the simple fact of polyamory almost always seems to be shut out, as you pursue the tree branch to get to the end of the romantic storyline with a Liara, Garrus, Morrigan, Anders, etc.
However, in the first Dragon Age there is a hint that it could have happened. If pursuing a romance with Zevran, and also one other person (with my first character, it was Morrigan), he will have similar dialog to anyone else in the instance of following a dual-romance: you need to break it off with them or me. How he phrases it is very different however, as he pins the blame on the other party, as they would be too jealous and just muck up the entire process.
(The above lovely fanart done by *sandara.)
It would seem that Morrigan might be open to such, but despite her free-spirit ways, she does admit to a certain sense of possessiveness. If one continues on a path with her and goes through the epilogue, and later Witch Hunt, she will discuss further her views of love, and come across as someone who has kept people distant to save herself. Early Morrigan views love as a weakness that makes people susceptible to all sorts of silly behavior and means they will compromise.
Zevran? He was born in a whore house, is perfectly willing to engage in threesomes, and talks about sex at a great length. While this has drawn various criticisms to him, he is very much a Lothario. I have written about him thrice so far: once looking at his construction as a character, another with the romance I had with him, and the other time as a representation of a bisexual male character. Depending on whom you ask, he’s a stereotype of what one should expect from a male same-sex romance option, or someone whose construction fits rather well.
The fact that he is also open to polyamory and queer in some sense of that word is also not that large a surprise. Again, depending on the queer friends you have, you’ll encounter various mindsets, and two schools of thought are that LGBT people are capable of the exact same relationship constructs; on the other hand, there is the thought that they are able to break free from a system and explore alternative options.
Zevran just so happens to be stuck in a game world, where unless an intrepid modder does some work, he cannot have that poly relationship with the Warden and whomever else the Warden may desire. If the player did such, it would also bring up the question of what form of a relationship would it be? A triangle where everyone is together? A V, with the Warden being the crux of that particular relationship?
Dragon Age 2 did take the step to allow characters to interact with themselves and to have lives that did not necessarily revolve around Hawke. If a romance is pursued with neither Isabela or Fenris, they pursue a relationship, which seems to be mostly sexual, by themselves. Again, considering Isabela, it would seem that a polyamorous relationship model could possibly have been open to her, but we are denied the option due to the system in place.
Therefore, we are now at a step where BioWare has given us options of characters who could likely be in a poly relationship on some level, but the system and toolset in place are not supporting it as yet. Then again, the argument could be made that systems tend to resemble our own, and while poly relationships have existed throughout history in one form or another, as the main set of relationships, they’ve rarely been highlighted as desirable in modern times.
The question would then become how does one create a system that supports poly relationships on a level, and how would that change the writing? Instead of writing a simply linear romance that could end up in couple of ways (here I am thinking of the hardened paths one can take with certain characters like Leliana or Alistair), there would have to be that option and the option to allow for either the romance to acknowledge another path being taken, or somehow merge the romances together. In terms of the systems we’ve seen thus far, I imagine a V shape would be the most likely (and this is assuming that the first step would be a poly relationship that is just three people).