In my first marriage, the we had veto power--the ability to deny a partner from getting involved with another person. I never used it, and she used it almost constantly. It wound up becoming a source of severe friction between us because it had turned us into a de facto swinger and a mono.
Comparatively, K and I have been together now for slightly longer than that total relationship lasted (and married for the last year and a half), and I never suggested veto power to her. K is solidly mono, and I now (compared to earlier when I didn't know the terminology) openly self-identify as poly. We never discussed veto power because K and I are very blunt and open in our communication. If she has an objection ("She is nice, but she needs to sort her home situation out before you proceed," for example.), she states what it is and why it's a problem. Having K around also encourages me to have quality standards such that I'm not as willing to accept crazy situations or someone who just patently would irk K. (Luckily we are similar in what irks us, so this is not a big stretch.) By me taking K's feelings into consideration and her proactively and clearly raising and detailing any objections, we are able to proceed with few major issues.
I'm not saying that the concept of veto power is a bad idea. I just found that clear communication and consideration means that veto power is moot. And a veto without an explanation is a definite sign of poor communication (a poly no-no) and likely a sign of some deeper issue.
Best of luck.