I am one of three and always wanted a 3rd, even though I am not a natural maternal person and work full time. DH wanted to stop at 2 (he is one of2) and really it made more sense to do so, especially as DC1 has some special needs. I agreed for a while as I was working on a big promotion at work, DC1 was being assessed and DC2 was clingy. Once DC2 was 3 I thought, it is now or never, and we threw caution at the wind and went for it. Well, best decision ever. To me, our family feels right and complete. DC3 has been the easiest baby and I have loved looking after him, and really enjoy having him.
I am way more chilled with him because he is not my first and I am not also looking after a toddler. Because of the age gap, the other two play together and are more independent. We kept our cars as they are as DC1 is big enough for just a booster so we all fit (tightly) in a Clio and Laguna. We have a small 3 bed house, so one room now has bunk beds. I shared with my sister til I was 11, no big deal to my mind. We organise the logistics a bit differently, but really, no biggie. The extra cost will come from full time nursery for 3 years until he starts school (at £1k a month, ouch, but that is just for 3 years. Out of a whole life time...). I have often heard it is double the work, well, for me it hasn't been (so far), even though we have no family nearby, but it depends on the gap between the children. As for the attention, well, I heard my mum describe to DC1 this summer that love is like light, the more there is the better it is :)).
As for middle child syndrome, well I was the middle one and I really believe I got the best deal! You are not spreading yourself thin with 3 rather than 2. The only matters you need to consider are 1) can you love another child? 2) can you reasonably afford it? 3) does your partner want it? Any other considerations are not really important.
When I announced our 3rd most people thought we were crazy, then many admitted they regretted not having a 3rd. As for the money, it is all relative, I was chatting to a friend this afternoon about her SIL who has just spent £16k on 3 rounds of IVF, sadly without success, and whether she should go for one last £4k round. Without going all sentimental, a child is for life. I look at my parents and the pure joy their 3 kids (and 5 GC and counting) have brought them. They financially struggled when we were young but now declare themselves full of riches.