I do this on my own about half the nights, ages when I started were 4.2, 2.1 and 8 wks. Even with a year of bedtime for three under my belt I still think it's hard, but definitely managable.
This is my typical arrangement: leave DS1 and 2 in front of video while I change DS3 for bed (he rarely gets a bath). leave DS3 while I bring the elder two up (the good alternative which works sometimes is that I put on an episode of something and tell them to come up when it's finished - and sometimes they do).
Feed DS3 (BF) in bathroom while 1 and 2 fight and pour water down the side of the bath (or alternatively DS1 teaches DS2 the alphabet using foam letters).
Put DS3 in bed, get DS2 out - brush teeth, PJs, story (often in the bathroom while DS1 was younger, now on the landing), he goes to bed.
Get DS1 out, teeth, story, cuddle, bed.
sometimes I do #1 & #2 at the same time as each other and they share the story, but that tends to get more fraught. Sometimes I do #2 & #3 at the same time (feed #3 while #2 gets a story), but #3 doesn't settle for his feed.
when DS3 was younger, I'd often save feeding him for last - a battery baby rocking chair was a godsend.
When I'm feeling particularly tired I pay a local teenager to come and help - the elder two love that. It's a fiver well spent - costs the same and better for my health than the bottle of wine afterwards.