Whether or not it develops to sex with some or all of them, what should you remember to do when writing a harem-type scenario where multiple girls are interested in the same guy. I know some of the obvious stuff, like making sure that the girls are distinct, for example, as well as making sure that the guy isn't a Marty Stu and giving the girls plausible reasons to be attracted to him, but for those who are familiar with these types of stories, what are the other key points to remember?
Keep in mind basic sexual psychology differences between men and women.
It depends on the era, and culture. With the caveat that nothing applies to everybody and you can find some 15% of just about any population that is non-typical, I will speak in generalities for a broad question.
Across all eras and cultures, including my own American culture, the one pretty consistent "feature" of a man that attracts many girls is the appearance of power and wealth, often manifested as fame in modern life, or high social status (elected office, or running a large company). Battle prowess is also high on the list.
It is why the fantasy husband is a young Prince in Shining Armor: High social status, high wealth, able to defend.
In the psychology of both men and women, sexual attraction is driven by the suitability of their partner for mating. For males, they (subconsciously) seek a woman that will bear many healthy children.
So men (in all eras) have an ideal woman that is young, healthy, and without flaws (flaws can indicate disease or a poor immune system). However, "healthy" depends on the perceptions of the culture; a few hundred years ago thinness could be a sign of disease and insufficient nutrition, so fatter women with larger breasts were considered the ideal of beauty.
Beauty itself (being pretty) has been shown by numerous psychological experiments in recent decades to be primarily driven by perfect facial symmetry and "average" measurements of facial features within the culture; it means the most beautiful men/women have symmetrical faces, and nothing of the dozens of measurable sizes is too big, too small, too far apart or close together. "flawless" means perfectly average! (which is difficult to achieve on every feature, so perfectly average, or even close to it, is rare).
That in turn has been found to be a good predictor of life health and a strong immune system and lack of disease since conception. Beauty implies both good genes, and a healthy dose of lucky circumstances in avoiding common diseases or lack of nutrition in the womb, etc.
The ideal mate for a woman (subconsciously) is a good provider (wealth) and defender (battle) with high social status that elevates her within her own tribe / city / society / country. Of course in her ideal the man is also fit, strong, symmetrical, tall (another indicator of health throughout gestation and childhood), but these are icing on the cake. The most important feature, to provide for her and her children, is wealth and status. Battle prowess is still important in cultures where violence is common, but in much of the modern world that is completely unimportant, and wealth and high social status can simply hire the muscle to meet this requirement.
As far as jealousy amongst the women is concerned, that does not seem to be as fundamental to women as it is to men. Although monogamy is common in most of the world, remember that a few hundred years ago polygamy was the standard and most women, in part by their own writing from the time, were comfortable with that. There are modern examples of polygamy, even in the USA (though the male is not legally married to all of his 'wives'), and it is advocated by multiple major religions (and prominent in the Bible).
Men have always been jealous of female infidelity. For a man, putting love and trust and DNA testing aside, there is no way to be certain a child is his own seed, short of personally imprisoning his mate. (He might know it is not due to some heritable genetic trait he does not have, like skin or hair color). Obviously for woman (putting high tech surrogacy aside), any child they birth is their own, and they know if they have been faithful to their husband. Thus, centuries ago, the use of chastity belts and the subjugation of women.
But women demanding monogamy from men is a more cultural phenomenon, something they have been raised to expect and demand. This means a man can likely find women that do not mind being a member of the harem as long as the man has the resources for, and is committed to, providing for them and their children for life. Remember what they subconsciously seek: resources, protection, social status, life security. So although the super majority of women in modern society may be looking for love and physical attraction, there is always going to be some small subset for whom the psychological basics are more prominent.
Which is why famous rock stars and sports stars and actors can have groupies or dozens of girls that know they are not exclusive and don't care very much. Which is why, even without sexual harassment, rich young men can do the same, or rich old men, or men with fame and high social titles in general.
I am not saying jealousies cannot be a big (or main) plotting factor in a harem. I would tone down the "monogamy" type of jealousy and focus on the "status" type; to be the husband's favorite wife, jealousy that one woman is chosen by him more than any other. For example, in some diaries of women of status in centuries past, that their husbands had mistresses was known to them and not a large concern of theirs. In most cultures several centuries ago, men (particularly wealthy high status men pursued by women) were thought to be emotionally incapable of resisting the sexual advances of women.
However, what they did worry about was if their husband's gifts to these mistresses became extravagantly expensive (like apartments to keep the mistress in) signaling a threat to their own status, treatment and resources. So, the woman's objection was not about their husband bedding some young mistress or three. The woman's objection was to any erosion of her own status and value in the eyes of her husband.
To forestall debate in comments: As I said, nothing is universally true in any era. The above is based on extensive reading of my own in non-fiction psychology and history, but ultimately my take-away from this is my own opinion of what to "keep in mind" if I were writing about a harem situation, how to make the male character a plausibly attractive partner, and how to make the females plausibly comfortable being one of many wives. These are obviously hot-button topics, if you disagree with my opinion, feel free ignore it. This is how I would write it.
Not sure this is a good question as it produces a list of unconnected points as an answer...
Since "harem" in this context is usually one man, many women, and the women are generally young I'll use "man" and "girls" in my answer for convenience. But I do not intend to say anything that is gender or age specific so anyone who is bothered by that has my permission to do mental substitutions.
Marriage became romantic fairly recently. Fundamentally it is an economic arrangement to form and support a family. A sustained harem setup has to work for its participants or they will leave or argue until the group breaks. For each participant think about what is the benefit of the situation to them. How does girl A benefit from girl B being around? How does the man benefit from not being monogamous? The benefits can be emotional and seem irrational but they should exist and be integrated to the characters.
A semi-famous example of seemingly irrational : Economic decisions made by fund managers and such seem irrational if you assume they are trying to make profit. Actually they are primarily trying to not lose their job or trying to get promoted or get a bonus or whatever personal reason that is opaque to outsiders. This is why bad bonus systems or performance reviews are so dangerous. People will optimize for what is important to them personally at the expense of what is good for the employer.
Common tropes are a girl who is avoiding an arranged marriage or a boy-girl insecure about her femininity. In either case a relationship shared with other women can be more secure than a more normal relationship because there is less pressure on their insecurities. Having an excuse and a scapegoat for your relationship not progressing can be highly valuable.
Polygamy is NOT an option, it is what you already have.
Strictly monogamous people would not be members of a harem setup. They have issues even reading about them. (So, NOT part of the target audience.) Characters can be uncomfortable about sharing. They can have religious or moral reservations about non-exclusive sex or marriage. Those reservations can also be very strong. But they have already chosen not to reject being a part of a group where one man is shared by multiple girls. Or more commonly will do so during the story.
This means that they do not think that caring about someone is exclusive. That is the fundamental question, the rest is simply a matter of degree.
You need to remember this even if the situation never develops in that direction or develops to a more conventional monogamous relationship. This is because the option exists for your characters and has an influence on their actions and decisions. To put it bluntly, otherwise the girls will either leave voluntarily or become enemies. It is the unstated and even publicly rejected hope of peaceful future together that allows them to coexist.
(n-1) times n is greater than n, if n is greater than one.
Or in other words, if you have more than one girlfriend at a time there are more relationships between them than you have to them. The man is probably the main character of the story but the harem aspect of it is mostly not about him, it is about the girls. What they want and decide is more important than what the man wants and decides.
One of the few gender asymmetries is that women generally do not think highly of the ability of men to make decisions about relationships. For your typical harem MC they would be justified to think so. Even so, nice girls will try to ask his opinion before making decisions about things directly impacting him. But realistically they will occasionally slip and the man will be informed of the decision afterwards.
This also applies to conflicts. Conflicts between girls will be more common and relevant than the conflicts the man has with them.
Non-exclusive means non-exclusive
People more comfortable with one man loving several women are more likely to see no issue with one woman loving more than one man. Social norms are usually different for men and women, though. In a setting where polygamy is the legal form of marriage, the asymmetry will be even larger and respected by law-abiding women.
Personal insecurities can be an issue even if the society is fine with it or the group is already violating the social norms. Almost all modern societies derive from agricultural societies with patrilineal inheritance. This means lots of men are deeply insecure with sharing women and not being certain who the father of the child is. This annoys egalitarians but IMHO it is perfectly understandable. Such values change with generations and it hasn't been that long since the identity of the father was of critical importance.
The larger the harem, the more likely it is the group includes a bisexual or a lesbian. If admitting you like other women would have real consequences, a private environment where pretty girls outnumber men by a large factor isn't a bad alternative. And the issues men have sharing women do not really apply to sharing with women.
Unless the group is insanely large you can probably ignore this. But it is a point that homosexuality makes groups with uneven gender ratios more stable. So you should probably think about it. And some of the characters should probably think of it at some point as well.