is the cost of an additional kid ever more than additive?

I assume OP means “when would the second child cost more - or having 2 cost more - than just 2 times the cost of having just one child?” I.e. incremental cost is not the same or lower than the same cost for the first.

The best examples above are when you bump up from 2-bedroom to 3-bedroom, or need a bigger car, or you have enough kids that you tip over into the situation where you lose one income.

The US at least is set up for a family unit of 4. Generally cars seat 4, drinking glasses come in sets of 4, 3 bedroom homes, etc. 3 kids is a lot more expensive than 2 if you have to do anything like buy a bigger car or house.

Seconded that special needs kids are exponentially more expensive. Especially if insurance does not cover things like therapy at 100% or even if you have insurance. And it’s often not possible for both parents to work with a special needs child in the picture.

I think the question is whether the cost of kids is more than directly proportional to the number of kids. We’ve seen that sometimes it is less, for instance with hand me downs. If you move from an apartment to a 3 bedroom house adding a second kids doesn’t cost any more.
What kills you is a step function. A third kid can share a room with a previous kid of the same sex, but if you outgrow your car and need a van it can cost, and if you breed like a rabbit eventually you’ll get into the next level. Our house has five bedrooms because the previous owners bred to the point where 3 bedrooms were not enough.

I’d say that in general the increase is less than linear, because of the hand me down factor and because you get smarter. But it breaks down for large n.

Many family houses in older neighborhoods of cities I or family have lived in, don’t have three (or four) bedrooms. I usuallly see two; even if three that doesn’ thelp with three kids (parents in one bedroom, so if the rooms are small, as they often are in old areas, where does the third kid go?). A friend in an old WWII suburb of DC recently had to raise their roof and add a floor when they had the second kid, as the house had only two bedrooms.

Right, but I assume the first kid also had those costs at that age, but i see what you are saying.