The family unit is the first and most basic part of any society, upon it rests everything else. It is therefore of vital importance to understand how the family’s of a society function to understand the society.
As always, never assume that the way things work for you is how they work everywhere, nor how they will work in the future.
The first thing to think about is where the society draws the line on what the family is allowed to do. Some have almost no limits, the parents or guardians can do anything they want including abuse. Others might see children as a trust that must be raised with the correct morals or they will be taken away with little due process.
The purpose of the family unit is to raise productive children and to produce and protect wealth. While there are certainly going to be exceptions to this as a rule families tend to be shaped to do both of the functions as best they can.
Think about the average lifespan of your populace, if it’s short enough then often you won’t have parents raise their kids to adulthood. It will have to be someone else. This was true of America if you go back to pre-victorian times. It was common to see older siblings and one or two step parents raise children.
While it rarely comes up you also must think about the gender mix. You might start to see family mixes that differ from what we would consider normal if there are many of one gender. This happening over one generation is not unusual. Whenever you have a big war, a large number of men die but you rarely see even a small dip in the number of women. Because it is temporary normally, by the next generation nothing changes.
That does not always have to be the case. If you had a very large difference, something like 10:1 then you could start to see different types of families pop up. It would have to be something that lasted a couple generations but it could change what they consider to be the normal family.
For example in The Moon’s a Harsh Mistress by Heinlein (can’t recommend this book enough) the moon is a penal colony, mostly political prisoners. The first several generations are mostly men, like 1:9 or worse. This means that most family’s have more multiple husbands per wife. This has echo’s everywhere in their culture, as it should (you really don’t want to assault a women on Luna).
However there is the second point, economic. The second purpose of a family is to create and protect wealth. If life becomes hard enough you could start to see love and romance start to mean less when looking at spouses. You could even see group marriages start from this basis.
If the average person had to work fifty or sixty hours a week just for a sustenance living, with no time to raise kids, a three way marriage might start to look good. Two people work full time, one works part time and takes care of the kids.
One last thought. Just because the desire to reproduce is part of the human condition does not mean its not a choice. There are reasons developed countries can have very low birthrates. While you can look up untold papers on why this is the case it all really comes down to incentives and costs (not just money).
Think about what the average person values, then think about what is given up when you have children. If the cost is too high then you will have a smaller birthrate. In Japan and South Korea the birth rate is very low right now, to the point of causing major economic problems down the road.
The family unit is so basic to the human experience that its a good way to make it clear that a people are different. Changing it is a good way of showing a people are human but very much not American or Chinese ect.
For example what if you started a book off with your main character meeting with his family. Except he had three parents, his two fathers being business partners who worked well together but did not really like each other. Then you say that was normal, and mention how few women there are.