They just have to allow polygamy and problem solved.
I wouoldn't be so sure about that. Even if that world legalizes polygamy, you only get matters like marriage, guardianship for kids and such out of the way. Those are important, sure, and a key point for general acceptance. But for daily life you could mostly do without that. The key point with any form of polygamy - legal or not - is that all involved persons, especially the women, have to agree to it first and the girls really need to be fine with sharing their man on equal footing. They need to have good chemistry, otherwise rivalry will make it problematic. And sooner or later jealousy and envy will show their ugly faces.
It MIGHT work for MC, Koumi and Mizuho... that said, the MC would first need to develop love and care for both of them equally. Also, the girls are friends right now but that doesn't necessarily mean both of them would merrily accept to take part in that kind of relationship. Maybe one of them is fine with it and the other dislikes it. That wouldn't work. And we are not even talking about some random "thieving cat" like Seira who is completely unrelated to Koumi and Mizuho.
If that world already had a long tradition of polygamy it might be different, but introducing it would solve some problems and create new ones.