My father's the oldest of 8. He remembers growing up as part of a huge family as - and I quote - "hell". His youngest sibling is five years younger than I am - and my DF was 26 when I was born! He and each of his siblings individually made the choice, with their husbands or wives, to have small families because of their joint experience of growing up as part of a large family.
My Godmother is also the oldest of a large family - she has 5 siblings. When she was 14, her youngest brother was born, and she was expected to take him out and about in his pram. She says that it was horrifying how many people assumed that her brother was actually her child, and villified her for it (small, rural town). People who had known her for her entire life, who had known both of her parents since they were babies themselves, gossiped about how my Godmother's parents had "had" to take in their 14 year old daughter's child "as though he were their own". He was their own child. People didn't want to grasp the truth though.
OP, if you have children old enough to be "independent", then understand that - especially now, when children of 11 are having children of their own - if you have another baby, they may well have the same suspicious stares and gossipy whispering as my Godmother did. And if you have a 4th, then what's to say that you won't want a 5th, and then a 6th, and so on... I do understand the yearning to have a big family. I'm the youngest of 3, and have two children (should be 3, but my DS's twin died in utero). I've thought long and hard about having another child ever since my DS was a baby... but I also know that it wouldn't be fair on the children I do have, those who are already here, for me to do so. It would be selfish of me. And it would disrupt their lives, and it may well hurt them. I also know how my DF and his siblings all felt at being part of a large family. And how my mother (the oldest of 4) felt.
You are already blessed with 3 children. Think of how they'll feel if you insist on having another child. Are they not enough for you? Y'know, one of my DF's brothers (number 3), actually felt as though he and his siblings weren't good enough for my grandparents. That that was why younger siblings kept on being produced. It left them all with huge issues that took years to either be dealt with, or come to light. Don't wish that on the children you already have, OP.