[Contains spoilers for The Book of Firsts.]
The first two reverse (female protagonist) harems I really recall encountering are Ouran High School Host Club and Fruits Basket. In both of these, a relatively low-key but likeable girl encounters a whole bunch of attractive and outlandish people, and ends up with one of them (arguably Fruits Basket was only ever a choice between two people, but I think the even more common trope of love triangle falls into this discussion anyway).
In both of these stories, the eventual romantic choice was Not My Ship, and significantly lowered my enjoyment of the story. The challenge with any of these romantic harems and love triangles is to get the reader properly invested in the 'correct' choice, so that they're not too annoyed at the ending. Meanwhile, I rarely read harem/triangle novels because I get frustrated by the time invested in the 'wrong' choice.
[Otome] visual novels/games are the complete opposite approach. In these, any of the main characters encountered can be pursued, and it's simply a choice of which route you take. The protagonist is often a cipher - sometimes even depicted as a faceless (though usually brunette) outline. This works not only to allow for a better self-insert (for those who like their romances that way), but also allows the protagonist to not be an obvious mismatch with any of the widely diverse characters.
Visual novels also reward players for following all the routes, sometimes unlocking hidden characters only accessible by successfully romancing everyone else you've met. I occasionally enjoy visual novels/otome games (I prefer the ones with daily life task structures over ones that are pure text), but it's rare to never that I'll play all the routes because there's always likely to be one that just doesn't work for me (like a Shotacon route, for instance).
'Menage' gets me over 60,000 search results on Amazon, so it's not an unusual sub-genre, though a fair proportion of the stories seem to be erotica. Most of the stories I seek out to read aren't focused around sex (though I did read an (at the time) fascinating series called "Blade" when I was in high school, which was basically 'go have sexy adventures' - and I thoroughly recommend 'Oglaf' for sex-based humour). I think menage (sex-focused or not) combines a couple of the challenges of harems and visual novels (particularly believing multiple people could be the 'right choice'). Monogamy works for a lot of people, and cheating is a distinct issue for many readers. You also need a reason why multiple eligible people would 'settle' for sharing their love interest.
Now, I won't pretend I sat down and thought all that out before starting Firsts, since my approach to writing tends to resemble the way the 'fog of war' clears from gaming maps - I start with a scene and explore outwards, and often don't even have a goal before half the map is cleared. I wasn't even certain if I was writing a menage, or a monogamous romance that happened to have multiple partners on the way. [I was even doing a bit of a feint with Carr, who could have been mistaken as The One.]
Anyway, I thought those who liked Firsts would enjoy detail of some of the more deliberate decisions I made during the process to make the menage ending more acceptable.
First Girl Wins
TV Tropes has a trope for everything, and First Girl Wins (gender flipped) is extremely common (especially in the Chinese web novels I've been consuming recently). No matter who else is introduced, the first eligible (for your gender/sexuality) person to be introduced is by far the most likely to be The One.
Mika meets the Kings as a group. That was very important, because if she'd met any of them first, you'd read the story differently.
In this over-the-top (though not quite Ouran-level) frothy setting, Mika fits many of the tropes of the visual novel protagonist. She's a brunette who is from a significantly less wealthy background than many of the people around her. She's a newcomer, giving her a level of detachment and distance from past entanglements.
Mika also has some very specific traits that make it possible for her to fit romantically with any and all of the Kings. She's so smart and self-collected it's hard for them not to respect her. They align in a number of ways (gaming being important to all of them, sharing a tendency toward the cynical while remaining fundamentally decent people). Mika is also adaptable, and is used to analysing and getting along with people, while also being possibly _too_ detached. She's sociable, but primarily focused on her personal dreams, and inevitably has to keep some part of herself back in order to shield herself from constant separations. She also enters a situation where she's supposed to treat Rin, Kyou and Bran equally.
But possibly most important is this song from The Whitlams (you'll know the line when you get to it - second half of the song), and this song from Tim Minchin, which leads us to our next point.
Meggan is very important to the story. Rin, Bran and Kyou have been friends from infancy, and bonded in a relatively (pun intended) hostile environment. They are inseparable, and that poses a problem romance-wise because when childhood friends grow up, they tend to go build separate lives (unless they end up marrying each other). The situation with Meggan, who Bran has long regarded as The One, is the in-story demonstration of this problem, and since the reader is (hopefully) invested in the bond between the Kings, Mika suddenly becomes not someone trying to have her cake and eat it too, but a solution. A way for three boys who are (primarily) sexually attracted to women to have a romantic relationship without their own bond diminishing.
Since I'm someone capable of publishing a book called Gratuitous Epilogue, it's probably no surprise to my readers that I'm enjoying exploring the 'what happens next' of the story. Deciding you want something and making it work are two very different things, though the characters are at least all smart and motivated. I am, however, 22,000 words in and on Day 2, so I am somewhat daunted by how much of what happens next I seem to want to tell. [It'll speed up a lot - just need to get them settled in their new situation first.]
Considerably less sex in this book! Many more relatives.
Fun facts: When I was thinking up names for characters in Firsts, I named Kyou for Kyoya in Ouran. Guess people get an anime feel from the story for a reason. And Mika's dad's surname is Teyrn - which is Welsh for 'king'.