Can I blow your mind?
There are no conflicts within the harem genre, because if there are, then it's not a harem. You see, a harem works when the girls are amicable with each other and are there for the MC. The moment that the ecosystem is disturbed, the member should and would be ejected, because it disturbs the peace and equilibrium. Which MC would put up with always having to deal with issues with their harem and their bitching? None.
If you want to look for drama caused by a harem, you need to watch Korean/Chinese imperial dramas and stuff. Where the story is centered around the powerplays in an imperial harem to make their own heir the next emperor.
But don't look for that in regular harem stories, because it's simply not what a harem is for.