I do have hierarchical relationships - Fly is the man I live with and raise his child with, who I currently consider my only primary. Punk and I are secondary for each other, as we both have primary relationships. Moonlight is secondary right now, but as I get to know her better, I can see her perhaps becoming more of a non-live-in primary for me.
Fly and I don't have veto power over each other. The only veto-type situation we might encounter is if someone is putting our kiddo in physical/mental/emotional danger or otherwise impacting him negatively. There was a period of time where he dated someone who influenced his behavior in such a way that it damaged the relationship between he and I. I never told or asked him to stop dating her, but I did reserve the right to say, "X, y, and z is happening, and I don't want to live like this. If this is what you want, then you and I need to renegotiate what our partnership looks like, or perhaps dissolve it." It was then up to him to make decisions about what he wanted in his life, and he and I ended up changing some boundaries, and he came up with some new boundaries with her that made us all more comfortable.
Although we've never explicitly discussed it, I am fairly certain Punk's wife has veto power, simply because she is the dominant force in their relationship. I don't think she'd utilize it lightly, but it is
one of the things that makes me uncomfortable around her. It's also one of the various barriers that has kept me from taking the relationship deeper, because EVERYTHING (when he's available, where we can go on dates, etc.) revolves around her schedule - her stuff comes first, and he has to fit his stuff around hers. His lack of autonomy and their unequal power balance prevents me from trusting our relationship.
Moonlight is single, and operates more like nycindie as far as having separate lovers and relationships, so there's no veto to worry about there.
As new people come into my life, I expect all the people I'm involved with to have opinions, fears, frustrations, whatever, and those are important to me. But no one gets to tell me how to live or who to love