Because you've titled your post "Pitfalls and advantages of Polyamory?", I'd like to make a very personal statement on that theme.
Like pretty much everyone in the society in which I live, I grew up in an atmosphere of intense expectation
that "romantic love," as folks call it, must go a certain way. That "certain way" is centered on monogamy, or exclusivity.
The terms themselves are a little loose. Few people have ever been fully monogamous in the strictest sense (lifelong, exclusive pair-bonding), but most folks have tended to follow a "serial monogamy" course. (All terms can find definitions at www.google.com
.) There are also distinctions to be made regards "social monogamy" versus "sexual monogamy". A socially monogamous person will have one long term, committed, romantic partner, but may
not be sexually monogamous, per se. Anyone these individuals may be sexually
involved with outside of this socially monogamous pairing will be, at most, "secondary". They are not at the level of commitment and involvement which we generally call family, per se. Their outside sexual adventures may have very little intimacy other than physical/sexual intimacy. It's important to know that there is plenty of "grey area" in all of this. Some folks may have "secondary" partners as well as "primary" partners, and the distance regards social monogamy/non-monogamy can be rather small, while for others the gap is enormous. Some people even have social monogamy established with partners with whom they no longer have (or never have had!) a sexual relationship!
But I said this was to be a personal statement, so here goes.: I'm essentially married, though not legally married. (My state doesn't allow two men or women to marry each other; and I'm a guy essentially married to my male partner, Kevin.) Here's the personal part. Kevin & I have been a couple for roughly thirteen years. It's been a long time since our first kiss, and our first "sleeping together".... I'd like to stay with Kevin indefinitely; but I'd like not to have this mean the end to first kisses, etc. I simply don't want an end to "romantic" adventures -- and some of these may be with Kevin, but some may be with others.
So we've identified an advantage to polyamory here. If only because I'm really not interested in profound physical intimacy with people with whom I have no interest in other kinds of intimacy and the process of getting to know one another deeply, over time. Casual sex doesn't work for me, nor kisses that are chapter or book endings rather than beginnings. Because we are polyamorous, I don't have to think my romantic adventuring days are over. I can have my cake and eat it too. There's nothing like a first kiss! Or a third.
Another advantage is that I can have the support and love of a partner AS I go through the ups and downs -- and crashes and burnings -- of all my adventures, romantic or otherwise. Kevin held me as I cried when I went through one such crash-and-burn, and others here can tell similar stories.
Another advantage is that Kevin & I can openly discuss our attraction to others, without much fear that this will be taken to mean that we're less interested in each other.: We know that love or attraction doesn't work like apple pie does. Kevin doesn't get less of my affection when I share it with others -- but often gets even more! And vice versa. Love grows by addition, rather than shrinking.
Another advantage, if ever I should have a second committed partner, aside from Kevin, I'd not be left entirely alone if one or the other should either pass away or move on. I'd still be a part of "chosen family" of some sort (although, admittedly, the same could be true with a very close "non-romantic" friend). I should say here that I find myself feeling much more bonded with lovers than with "non-romantic" friends. I suppose this has to do with what we could call the "touch factor". I simply feel a special kind of closeness with people with whom I can lie with in snuggles and cuddles. Few friends of a non-romantic type have ever been able or willing to share with me in this way. Though there have been a couple of exceptions.
I'll have more to say on advantages over time.