I'm one of 3. I have 3 children. Some of the replies have made me laugh, in a nice way.
Some of the issues some people fret about really don't need to be a problem (and reflect very middle class privilege/attitudes).
Things I considered as key were: childcare costs, more years doing the school run, car size (as both DH and I drive and we run a car). The first of those was the biggest consideration. The car size ended up being the least as we decided we'd want a 7 seater anyway for the primary school years for our first two children.
Numbers of bedrooms? I shared a bedroom growing up and loved it. Loads of my peers shared bedrooms with a sibling too. My children have a bedroom each yet sleep in one room together most of the time. The rest of the time two are in together and the youngest is in with me and DH! We joke we'd have been better off with just one giant bedroom. Yes, this will change as my children reach their teens but still.
Costs such as university, driving lessons, etc? Well, if I had just one child and was loaded I wouldn't be paying for all their driving lessons anyway! Do teens not get part time jobs any more? I live in a city with good transport systems. University- it's not a given all my children will want to go to university or have the ability. Plenty of students work part time or in the holidays. Who knows what the costs might be when my children are 18 and who knows whether I'd be in a financial position to even send one.
Food - I spend about half of what another poster spends! I foresee this being a huge expense in the teen years, but childcare costs will have gone.
Clothes, shoes, etc. I save and budget and my kids don't get hugely expensive stuff. Shoes at the biggest expense. Clothes - In my circle of friends clothes are passed on and, of course, clothes get passed down between siblings, lots of reuse. Teens will want more new stuff, I'm sure but if they each have slightly fewer items in their wardrobes than if I had two, then so be it! As long as they have enough.
Activities - yes, ferrying three school age kids around is a logistical nightmare at times. But I consider that we're lucky to be in a position to afford after school activities, etc. Each child doing slightly fewer activities than they would if I just had two children is an incredibly privileged position to be in really, isn't it? And they do the same as they would if I had two. My DH AND I spend less on ourselves and we lift share with other parents to ensure that happens.
Holidays? We tend to go for self catering, camping, etc type holidays anyway. Places are getting more flexible on family tickets but also it's not like days out for a family of four are cheap and then that fifth child's ticket is hugely expensive, is it? So we budget for the fact it will cost us, for example, £35 instead of £30 - more packed lunches for example.
If I had been worried whether I could genuinely afford to house, feed and clothe three children then I would have stopped at two. But that was never a concern, it's been more about how we budget and how much money I'm prepared to spend on a teen and young adult. And, for me, I won't consider my children to have suffered in any way or that I've failed to provide, if I don't pay for every single driving lesson they have or they have to find paid work during their time at university. I'll still consider that my children will have had a pretty privileged lifestyle, much more so than mine was!
And the joy my youngest brings to us all means more than money and means I could never think of saying to another parent "don't have a third".
What I would say is consider how much you can juggle, how much can you add to your mental and emotional load of the logistics, and practical care of being a parent of three, how much attention can you give them all, and how would you cope if they don't get on? That all matters far more than anything else.