Similar to comments above there's a difference between poly and open. I've not tried either but I've multiple good friends who are in "monogamish" relationships and it seems to work pretty well. For them the non-monogomy is just fun they have with others, but ultimately their partnership comes first. Otherwise it's very similar to the monogamy you describe but with agreed exceptions to sexual exclusivity.

It's not for everyone and it takes a lot communication (and low levels of jealousy) but it seems to work well at providing the structure and stability of marriage without forcing the full sexual exclusivity that some find constricting.