What makes stories interesting is how people solve problems - What makes worldbuilding interesting is how societies solve problems
You don't want a solution that makes the problem go away - you want a series of band-aids that would evolve over time to patch an arrangement which generates problems.
If the firstborn is the heir, and multiple wives might be the mother of that firstborn (and most of them want to be), how would that affect society?
Casting lots to have the husband first?
Who gets the head start with the husband? (He's unlikely to be up managing half a dozen wives on the first night.) Well, some kind of competition seems appropriate. Either a (supposed-to-be) entirely random thing, like rolling dice or drawing straws... Or you could have something more like a chess match, or athletic competition, so the smartest (or strongest, etc) woman gets a day's head start.
Do you have the marriage on the day when the most wives are likely to be near their peak fertility?
If having the first child means your child inherits the lion's share of the wealth, the family name, etc... The subject of fertility, and signs of it, will be a subject of a lot of study (and of superstition). It may be considered "fairest" to have the wedding when the most women are most likely to be ready to get pregnant.
And bad luck for you if you're the wife who's not in the majority on that day. And bad luck for the impatient husband, if the sister-wives put off the marriage for a year or two, waiting for the most fair occasion.
Will 8-month-pregnant women take long hikes or do heavy exercise, trying to steal a few weeks?
Early births are auspicious births (if the baby survives). This only applies if multiple sister-wives were successfully impregnated at nearly the same time, and if it's (thereby) the first child.
On the other hand, some mothers might take the opposite strategy, going for a longer pregnancy, hoping for a healthier child who will live when the early-born child might not make it through childhood. (Infant mortality was quite high in ancient times - if you want that to be part of the story.)
Early-born boys might be seen as a mixed blessing
"Hurray! I had a son, and he survived! Our family will get an expensive dowry for him. But that means that Ayesha's child, a girl, will be the heir, even though she was born a whole 3 days later..."
It may be an obligation of the primary heir to marry sisters or cousins with particularly poor inheritances
If it is accepted practice for near-kin women to "marry," it might also be an obligation for them to do so, to otherwise protect some of their kin from poverty.
On the other hand, significant complications might arise if, on the primary heir's death, the next in line inherits (and not the wives of the primary heir, if they haven't produced an heir for the next generation yet), because that means a whole group might suddenly go from being head-group of the family to being something else.
So maybe the stabilizing obligation cuts the other way, and the first 2 or 3 heirs in line will (traditionally, but not be required to?) marry, to prevent such uncertainty.
Or maybe the current heir in a given marriage gets to make or tweak any/all of the above rules... But if one of the sister-wives still manages to have the first daughter, that's still the next generation's heir.
Complex rules with obscure exceptions are great for story-tension... As long as it can all be communicated before it becomes important to the story, without boring or confusing the reader.