I had never considered poly but 4 years ago at a previous job I was working with a girl, who I'll call "A", and we ended up developing a mutual crush and eventually starting a relationship. She was polyamorous and already had a boyfriend, who she had been dating for 10 years at that point, and they had been poly for about 5. Both had started new relationships over that time so they were pretty experienced and able to handle it by the time I came into the picture. At first my relationship with A was pretty casual and basically just an FWB situation. We both knew she was leaving for grad school in 6 months so it sort of had a timer on it. We split up amicably when she left but ended up getting back together 3 years later when she moved back. The whole time her boyfriend was very cool to me and I didn't feel like I caused any tension between them. The fact that they had a long established relationship definitely helped I think. They became poly because they both wanted to: he had been a virgin when the relationship started and wanted to experience sex with other people, and she wanted to explore her bisexuality. I do agree with some of the posters here who see a lot of poly relationships that are only really wanted by one partner. Obviously that will make the other partner unhappy and is untenable long-term. Anyway A and her bf had a very secure, drama-free relationship which definitely made it possible for me to come in without disrupting things.
Anyway about 6 months after getting back together with A, I met B on Tinder. She had never been poly but was open to it. I put that I was poly in my dating profile so she knew upfront. We ended up dating, and there was definitely an adjustment period where A felt a little jealous and needed reassurance, and B felt a little intimidated by the existing relationship. But we communicated through it and A and B ended up becoming friends and even hooking up a couple times, although they don't date each other. B has recently started seeing another guy and I've also felt some minor jealousy but honestly not as much as you'd probably expect.
Really it comes down to being secure in your existing relationship so that you can trust that a new partner for either person isn't going to threaten that bond. At the end of the day I know that both A and B love me even though they also love other people. Everybody shares their partner's heart anyway with their partner's friends and family. You already share their time with their employer and their hobbies. If you can accept that your love is real without being exclusive, and that your partner's feelings for another person don't change their feelings for you, I think it's possible. All people involved have to genuinely want it, know what they're getting into, and accept that it is what it is. You have to put in more time and manage your time wisely, you have to consider the feelings of multiple people, and for fuck's sake you need to get tested regularly and/or use condoms.
Also (perhaps stereotypically) none of the people in my polycule want kids, which makes it a lot easier I think. Poly with kids is a whole other minefield that I can't really speak to.