Honestly, I believe as long as you purchase extra BOff slots the number is unlimited. One guy in my fleet literally has dozens. I think he's flying Noah's Arc. I never got into details, but I think he's got one male and one female of every race.
50-something per character. I want to say 56 but not 100% sure about that.
Would assume that for a total on the account, it would be just a quick multiply.
According the STO Wiki http://www.stowiki.org/Bridge_Officer_Slot you were spot on about the 56 BOFF slot cap. I've got about 34 BOFF slots currently (with 17 filled). So, BOFF collector that I am, I've been mindful of that 56 slot cap.
"Don't try to be a great man. Just be a man and let history make its own judgments." -Zefram Cochrane
Vice-Admiral Methos Corinthian