I'm not comfortable with vetoes. I'm not comfortable with telling a partner "if you say stop, I have to drop everything" or "if I say stop, you have to drop everything".
However, in a case-by-case basis, I will take my partners' opinion into account when making decisions, and if my boyfriend told me that he's got a really, really bad feeling about a specific person, I might decide not to take things further.
What I would hate though is a veto that happens later on. What I mean is that I am fine with partners being "consultants" when a new relationship develops, but at no point is it fine in my book to tell someone "dump him/her, just because".
It's important to me that my partners get along though, so if they don't, it's likely that the newer relationship won't go very far.
I also have a principle I've always stuck to so far, and that is that if someone ever tells me "it's me or X, you've got to pick", I pick X, no matter what or who X is. Or really, it's more of a matter of "I don't pick you", because sometimes I pick neither. But I just can't stand ultimatums like that, they feel controlling and disrespectful of both me and X.
Now, if a partner tells me "You spend a lot of time doing X (no matter what/who X is
) and not a lot of time with me. I'm feeling lonely. Is there a way you could spend more time with me so I don't feel like I always come last?", that would be different. It's not an ultimatum, it focuses on what they feel and not what I "should" do, etc. Then I'll see about working things out with everyone involved so people are happy (including me).
For me, a veto is a hard rule that one person can just decide to step into another's relationship and break it off. That's not cool with me. I much prefer communication with everyone involved, and finding case-by-case solutions.
However, before there is any relationship at all, setting some harder rules might seem more comforting because everything is so new and unknown. So I can understand that. Guidelines you set to have an idea where you're going.
However, which any new relationship, or any shift within a relationship, these tend to need to be examined.
And after all, don't a lot of people start their journey into poly this way, by re-examining what used to be a hard rule of monogamy, because their relationship has evolved or it just doesn't work for it?