This particularly sounds like my situation.

My hubby is, unfortunately, not a very good judge of character (his words, not mine). He forgives too easily (you'd pretty much have to kill his brother for him to be angry enough to cut you out of his life), and is over all too trusting. We have agreed (at his request) to rely on me as...basically a compass for him. I would never tell him not to see someone because of something frivolous and he trusts me to give good reasons for whatever requests I make in regard to his relationships. I have rarely made demands (I did firmly tell him I didn't want him to involved with a particular girl, it ended up blowing up like I predicted it would and could easily have been a lot worse if she had lived closer), and, as I mentioned, would never make them without good reason. Once explained, he has always agreed with what I have said.

We have small children, and because of this, we have agreed that this relationship has to take priority over any others. So right now, I guess we're doing a more hierarchical version of poly, which includes, to some extent, veto power. Not only does that include individual relationships, but also on the whole poly thing. Should the situation arise where one of us felt that seeing other people was becoming a detriment to our relationship, our relationship would take priority and the harmful behavior would have to stop, to be revisited later at a more stable and healthy time in the current relationship.

The difference here, I think, is that our other relationships up to this point, have been much more casual and short lived. While neither of us have anything against looking for long term/life partners, neither of us has found anyone who we would be interested in bringing in in that capacity. So a short term partner is much easier to take a step back from.

Just wanting to add, he has just as much ability to say 'no, I do not want you involved with this person' and, with good reason behind it, I would absolutely listen (not to say I would ignore it without good reason, but it would be paused and talked through instead of just completely off the table, as would happen if he disagreed with my reasoning).