Oh god, this again.
Yes it's possible. Yes, plenty of people do it, and you only tend to hear about the unsuccessful ones, in the same way that you only hear about people's shit supposedly monogamous relationships on MN - almost nobody posts about how great and smooth their relationship is, they post when it's in trouble.
I've spent most of my life in "committed living-together primary plus one other deep emotional commitment" type relationships.
I don't think I have more or less love to give than others - what I do have is a lack of jealousy a good sense of security in my relationships, and an understanding that both I and my partners can very much love and be committed to each other, and also have similarly intense relationships with others.
Someone upthread said it's not the same as with parents, siblings, children, friends where you can love more than one at a time - well, for us, it is. I have never understood the mentality that just because you have a sexual/romantic relationship with someone, they must be the only one, whereas with all other forms of love it is reasonable to share that between multiple people.
Live your life however you want, but it's as ridiculous and judgemental to say poly relationships aren't as real or deep as others as it would be to say the same about same sex relationships, or age gap ones, or anything else you personally don't happen to approve of or understand.
And yes, I would also agree that there are many people who misuse the "poly" label to mean they want to fuck around, that their partner may not know or be coerced into it, or that aren't able to have multiple respectful relationships. But those things all occur in supposedly monogamous relationships as well - there are rubbish people in all strands of life.
And @ThisFluentBiscuit
"Part of me thinks it's all just a big joke and that it's just an excuse to get their leg over more than one person. But why not just have casual sex with others, then? Why get into a second deep relationship?"
How about because it's not in the least about "getting a leg over", but about the emotional intimacy and connection I have with a particular person?
I don't like casual sex, have had 3 partners in 15+ years, and value deep, committed and emotional relationships, as do my partners. It's just that apparently they're not in a format that you judge to be acceptable...