In our Vee, we technically have a "veto" rule, but I don't know that it would ever come into place - at least on my end.
The only time I'd ever even think about it would be if the other person were a disaster on wheels (no idea how to describe this, but I once had a friend who Vegas-married a woman who pretended to be the illegitimate daughter of John Lennon and Janis Joplin, tried to pass herself off as everything from a Playboy Bunny to a nurse to a racecar driver, tried to pull his daughter away from her mother, and wanted him and his friends to contribute money to "her cause" - helping children of celebrities. THAT is a combination of harmful and crazy that I'd run screaming from if I ever saw it again). However, if P were hell-bent on dating someone like that, I'd certainly tell him what my impression was, that I didn't want anything to do with her, and then reevaluate my own relationship with him if he started going down the cuckoo path as well. I wouldn't put my foot down and say "no", but I'd have one foot of my own out the door.
Laying down an ultimatum somehow seems to encourage either resentment or finding ways to sneak around it, neither of which I want to deal with, especially if it's a legitimate concern. I'd much rather just talk about it and take it on a case-by-case basis.
Luckily, P is pretty communicative (small-talk-wise, not privacy-violating-wise) about the people he sees, either as friends or as dates, so we seem to be moving well in that direction.
If it were ever turned back around on me (which I find highly unlikely
), and I saw no basis for it, I'd push back. No different from P telling me who can and can't be my friend, in my opinion. I would have to talk, at length, about WHY this is a problem, before agreeing to anything.
However, P and I never opened a marriage, do not have kids between us or a family "unit" that we feel we need to protect. That may make a huge difference to some folks. Your mileage may vary.
Mono. Divorced, two kids, two cats, one house with many projects.
My partner of ~3 years. Poly. In relationships with me, Xena, and Noa.
Poly. In relationships with Chops and Noa, and dating others.
Married, Poly. In relationships with Chops and Xena (individually).
My navel-gazing blog thread: A Mono's Journey Into Poly-Land (or, "Aw hell, there's no road map?!")
My slightly more polished blog (external): From Baltic to Boardwalk