I'm not quite sure where to start. It's not linear, or at least I don't feel like it was, when my third child was born it felt like there was a gulf between a family with two and a family with three and it felt like that gap looked like a big change in pace and intensity in parenting. It never felt like chaos though, unless we all got sick and then it felt a little like juggling plates.
I didn't need to rearrange the world in terms of routine because ds2 started school not long before ds3 was born. So he ds3 did have to adapt around school routines but still got those mega naps (and so did I 😁) and plenty of one to one time when he was a baby
School runs and clubs weren't harder to manage, they were at times of the day when babies are typically awake. I'd just put him in the sling and walk the kids to/ from school.
I don't think the older kids ever felt neglected. We kept their routines absolutely rock solid and you get into the swing of looking after a bunch of kids at once. Mostly it's just about keeping the kids literally together rather than atomised around the house. You can breastfeed and help with homework at the same time. Babies can play on the mat while you make Lego with the older kids. The youngest can be in the highchair snacking while you help another make cakes. You can entertain the baby while the other two play with each other. It's no big deal and I think this element is over-egged.
After maternity leave I worked pt for a couple of years then I took the opportunity to work pt from home. But, tbf, that was a decision led by health issues rather than juggling kids.
Now, 10 years later, it doesn't feel like that there's much of a meaningful difference at all in terms of parenting three over two. The pace and the requirements aren't and more arduous - meals are bigger, laundry loads are bigger and it's probably a little noisier.
At this point the biggest difference is financial. It isn't long before ds1 learns to drive and starts uni and then we are in it for almost a decade as they all follow suit. Which we can cover fine but doing it three times rather than two feels significant.
Yes, holidays have been fine for us. We always hire a place and go self catering anyway (and would do if we only had two because of dietary restrictions and pickiness issues) so that style of holiday typically accommodates larger families. I know other people who prefer package holidays do find it harder and far more expensive with three kids.
I think this is the longest post I've ever written. Fwiw, this is just my experience and you'll get wildly different responses.