I feel that this entire question is built on a fallacy--that is, the assumption that men don't like to share. There is a growing amount of evidence that men's hostility to each other when it comes to sharing women is cultural, though the jury is out on to what extent. However, bloodlines and inheritance rights (power and money) factor heavily into our western culture's hostility about shared mates, problems other societies don't have.
There is an existent matriarchal society in China where men have no issue in sharing their women, and in fact, know for a fact those women are never "theirs" to begin with. It's expected that the women will choose them to breed with, but may or may not choose them as a mate in the future. It's normal, accepted, like we accept monogamy as a default.
There's also a more primitive tribe who truly believes that every man who has sex with a woman is adding their genetic material to the created child. They share happily because more genetic material = stronger, healthier children, and the children always belong to the entire tribe, not just one man. This belief could easily be a spiritual one in a fictional setting, as well, that every man is adding his "essence" if not his physical features. If a child is raised by an entire tribe or group of people, that would essentially be true in a nurture sense.
The Hawaiians were real big into free love before the Christian missionaries wandered onto their island and taught them how to behave "properly." And they were, by far, not the only native peoples that had to be bludgeoned into monogamy by missionaries--the examples of such are many and vast. And if you look at erotic art from native americans, you'll find a lot of tribes were really open to threesomes, foursomes, and moresomes (as well as not having the body taboos we now have).
In fact, you can even see it today, right here in the west, with open relationships, polyamorous relationships, and men who just like watching their wives laid by other men.
So yes, a man born to the idea he would likely have to share a woman, with a culture that backs that idea, a man who knows doing so is part of his honor and duty is probably going to be just fine with it. Just like women have been for centuries, when told it's what they have to expect out of life and that's just the way life is. Even if they all had to share a bed (gasp) together.
I really feel before the question can be answered, it needs to be asked with more a bent to the facts that already exist. While yes, I think your system could work, basing it on "men don't like to share" is going to feel not only unrealistic to a lot of readers (historians, anthropologists, people who've been in alternative relationships, people who went to college and took an anthropology class), but honestly more than a little demeaning to men, with sexist undertones to women as well (women are cattle to be owned).
It's just...not a good scene.