There are some basic best practices when using Alt attributes (like not keyword stuffing, etc.) but as long as you are not violating any of those I see no reason you couldn't.

For example, tons of blogs use stock images (and many recycle old images they've already paid for). I may have one article about "Starting Your Own Business" and use a picture of a woman at a desk. I would add the alt text "woman starting her own business". Later I might write an article about "Impressing Your Boss" and reuse that same image with different alt text (ex. "woman impressing her boss at work").

Those are cheesy examples, but to answer your question, I don't see any reason you couldn't use multiple alt text on the same image. After all, "a picture is worth a thousand words" and not even Google can deny that.