No you cannot fight bosses multiple times in a single playthrough. I like to think it's because the rewards of the bosses are huge, and being able to simply farm them over and over would be too easy to rack up tons of quick cash.
Though this isn't the same as the actual boss fight you're referring to, you can sort of fight them repeated if you find their respective Obols, when you pray for a blessing at the shrine. You can do this:
once you've beaten the boss and given it's respective Obol to Charron, you are allowed to fight the boss again but with a fixed class per boss, and the boss itself has special powers making it a completely different and much more challenging fight. If you die during this fight you lose nothing and are placed in the same boss room. From here you can try again as much as you like or continue through the castle as usual. I myself haven't completed any of these, so I'm not sure what happens if you win this fight.