For most random fights (ie. blue slime) there isn't any depth, but there are sometimes specific monstergirls that have a side quest line to go along with them, where they form a relationship with the player. These characters have unique models, and sometimes have an actual quest in the grimoire. But for the most part you just find them as you wander zones. There are a couple in every zone. But It never really becomes a full Harem, since they don't really ever meet each other (as far as I know) and is instead just multiple independent relationships.