The three of us in our "V" identify as non-hierarchichal, although a little differently than CdM's example. We are actually splitting time in about as balanced a way as we can right now (my partner, the hinge, splitting time between two "homes). To add a little to the complexity, I'm Mono. My partner and his OSO are Poly.
It's working out pretty well, but there's a LOT of scheduling involved... but that's not your question.
Anyway, we do have a veto, but nobody's had an occasion to use it yet. For me, it's kinda moot, since I don't plan on dating. I personally wouldn't ever plan to pull the "veto" card unless the person were completely toxic (and even then, I'd probably put my misgivings in a "voicing my concern" way, rather than "here's my veto"). However, if my partner decided to have another "full-time" relationship, I am prepared to say that if my time needs won't be met, then I would probably have to pull out unless we could work something out... Less of a veto and more of owning my own issues, I suppose, although to some it would still feel like an ultimatum. I wouldn't intend it to be one, though...
No real pressure re. who to date. My partner is worried about his OSO's safety, of course, and wants to meet the folks she dates if it turns into something more than casual dating, but no real pressure on who to date or NOT to date. There are rules in place for safe sex (other potential sexual partners must get written proof that they're clean, must meet the other partner, etc. - which *I* wouldn't do without since my health is also at stake here), but no rules against it. Just a couple more hoops to jump through.
Hope that helps!