Eh, I think it is fair to point out that there is a certain strange undercurrent in this setting (only monogamy, gay people basically don't exist) which could be discussed......
I know I said that gay content wasn't feature above, but I wouldn't go as far to say that gay people basically don't exist the MGE universe; at least in regards to human to human relationships. I just meant that we won't be seeing gay content involving monstergirls. Here's some lines from Alp's profile.
"Alps are incubi that, deep within their heart, strongly desired to become a woman
or be with a man" (KC has said women are able to turn into incubi in a similar way)
and probably relevant "Their body has completely changed into that of a woman, yet they self-identify as men."
Someone can correct me if I'm wrong but I don't think even The Order has issues with gay relationships (at least I don't think it's explicitly stated anywhere). I also believe monsters aren't against gay relationships. They'd always encourage people who have feelings for another to get together and even assist them. It's just that for monsters, men (or incubi) are a necessity for sustenance, gaining power, and increasing/maintaining their population.
So I don't think for example that Kenkou would be against writing a story where a gay human couple are in love who then get monsterized and one either turns into an Alp (if men) or incubus (if women). (kind of already did though not about a couple,
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)
As for polygamy; if we're talking about the human side of things, possibly The Order doesn't like that because of their teachings against over indulgence of desire but even then I'd say it probably varies from place to place as the The Order doesn't control all human society. Especially with monster-friendly states due to monster influence (esp. multiple wives).
If we're talking on the monster side then polygamy is often encouraged. Would most monstergirls prefer to be the only wife? Sure but they generally aren't against polygamy and harems aren't uncommon. If you were refering to being "marked" by a monster, then that's about the same as wearing a wedding ring; it won't deter insistent/persistent individuals or if the man insists or is persistent (and the monstergirl also likes him).
If you mean a monstergirl having multiple husbands then yeah, only one husband for them (though it is explained that their bodies adapt to one man (the one they have the most love for; that love never fading) and also can't physically feel pleasure but instead feel disgust from other men).