Its surprising no-one's working on that, given Yammer is basically a SaaS Facebook.
Or maybe they are, but they can't be found. I've noticed this before, but you can't google for something like "SaaS version of Quora" because all you'll get is results - in Quora - about SaaS. Same for "in-house Quora". So maybe someone does offer a Quora-like product for the enterprise, but they're consigned to invisibility.
Askbot exists[1] -- its look-and-feel is more akin to StackOverflow than Quora, but it's pretty widely deployed[2][3]
[1]: https://askbot.com/ [2]: https://ask.fedoraproject.org/ [3]: https://ask.libreoffice.org/
Tangent: It has been 7 years since their founding. How does Quora make money?