One consideration that was largely missing from this thread is that of children. Poly is whatever you agree to, but parenthood is its own sort of commitment, with its own category of moral and ethical issues worthy of debate. Many parents will choose to maintain a structured household that prioritizes a stable family environment, such that polyamorous connections must be hierarchically subordinated ("secondary") and subject to extra restrictions. When kids are involved, it would seem to me haphazard to operate with the only rule being "don't be an asshole."
It is, however, an excellent place to start from. Don't be an asshole with your partner(s); don't be an asshole with your partner(s)'s children. In general, don't be an asshole.
I have been a child, of course. Frankly, I hated it, for many and varied reasons, but one that sticks with me is that I was an intelligent capable person crippled in my pursuits because I was
young. Other people -- adults -- often looked down and talked down to me because I was
young, and discounted my knowledge and experiences for that reason. Not all of them, thankfully, but far too many.
I am trying hard not to inflict this on my own children, in their own house; sadly the social attitude persists.
My mother was divorced. Dated, at times. Had live-in boyfriends from time to time. Remarried twice. When she went out on dates, I don't recall it ever bothering me. The live-ins, though, they usually bothered me by claiming authority in the household I didn't perceive them having or deserving. (At least one was nuts, but that's a different issue entirely). At least one new husband bothered me by trying to step into the "father" role; I had one, even if he didn't live with us, and marrying my mother didn't make the man my father. (Might have been different had I been more estranged from my father.) I felt pushed out of my house by the second stepfather, and it wasn't a good start to our relationship.
Had any of them consciously thought of their effects of their behavior/attitudes on me, things might have gone better.
So I try to do the same for my children, and those I'm around. Both of my partners are divorced from previous marriages, and have children from them. Liam's children are not much younger than I am; in the course of our 14 year marriage, I've tried to see what sort of relationship they want from me. Mostly, not much, and that's been fine. Jai has two adult children and one minor one; I've met them all, but not recently.
Liam and I have three minor children. Jai has met the older one, recently, but not the younger two, mostly due to timing.
Potentially, yes, it could be a tangle. But, not worse, I think than some of the situations I encountered growing with my mom. (After she divorced my 1st stepfather, we attended his mother's funeral. With her new boyfriend. It did not feel weird to me at that time, but threw others when I described it later).
I'm sure there would be resentment and problems if, say, Jai tried to act in a father role with my children -- but that could happen if we were in a more standard mono relationship by way of me being widowed or divorced.
Treating the children as people in their own right helps, I think. Letting them determine the relationship they want with non-bio adults is important. Or, for that matter, bio-adults -- I did a surrogate pregnancy, traditional not gestational. As they live across state, we mostly maintain an email friendship. But I've visited them, and they visit at least once every year. This was not determined by contract; by contract I wanted a yearly update with a picture. This is connection, and friendship, created by getting to know each other and having things in common as well as interesting differences. Our shared child, when she visits, refers to me as her mother. She also calls her mother, who raised her, her mother, as you'd expect. This is how she sees things, and we're all fine with it. We've become an extended family, with the shared child as a hinge.
So, anyway, I've rambled on quite enough now....