I have a friend who had her 4th at 39. Her kids are now 17, 14, 12 and 6.
I was chatting to her recently about things and she told me that her food bill has risen a lot in the past few years. She has 3 teen boys and they are always hungry.
She said as well since they went into secondary school the cost of uniforms, sports gear, lunches ect not to mention the cost of regular replacements as they are growing out of trousers, shoes and runners is high.
Then at times she could have 2 or 3 kids needing to be 2 or 3 different places at the same time and these place could be anywhere from 5 to 20 miles away from her home.
She sometimes takes turns with other parents getting kids to sports ect.
She said as well that as her kids have gotten older than they needed more help or own time just with her or her husband due to different things and at times she found this hard. She said that brining up teenagers now is far harder now because of the internet, online bullying and her kids are seeing other kids with plenty of money and no rules and they want the same.
It easier when your kids are small but the expenses go up a lot when they hit secondary school and the university stage is very expensive. I have several friends with kids in university and they have good incomes. They have told me the cost of rent not to mention the other bills. Most of there kids have a PT Saturday job but these are getting harder to find.
I think you need to consider it not just what you want but what's best for you and the children you already have. If you have a 4th child at 40 what age will your partner be? What happens if your next child has special needs? Not not all special needs conditions show up on scans. I know several parents whose kids have autism and other conditions and they have ended up either giving up work, working less hours or not been able to work due to a child's high care needs.
Then if you already have had 3 c sections your putting more your body through a lot at 40 having another one and this could lead to complications that will effect you long term. One poster here ended up with long term bladder damage.
Your also need to consider your own health long term because you already have 3 kids and you need to look after yourself so you are able to care for them.
In your situation I would stick with 3 kids and work towards giving them the best life possible.