Is the expression "to float someone's boat" possible outside of "Whatever floats your boat"?
Solution 1:
This expression by nature is very personal, so you'd never see a "formal" version of this expression. This is a light-hearted way to ask what someone's hopes and dreams are. It is about as polite as you can be for this sort of question. Asking someone what their passion is, for instance, might demand a serious response whereas "What floats your boat?" is flexible and allows a non-serious answer, making it all the more polite to use than an alternative.
Though that said, here are a couple alternatives: "What drives you?" "What's your passion?" "What do you do for a living?" (not precisely the same thing, but you might get an equally in-depth answer)
Solution 2:
At a job interview, I was once asked in this context, "what makes you tick?"