I hope I'm in the right place to ask that.
I am not asking a question about the technical problems (I imagine we will have to maintain and synchronize somehow different repositories, maybe with incompatible pull requests, but this question is for another day).
What I would like to know is:
How that would be perceived by the community at large ? Does it risk killing the eventual interest in this library?
I don't personally know of any library that works like that. I'm pretty sure it is possible however, but any evidence of such a library is welcome (successful if possible). That's also because I'd like to see how they present it.
More importantly, what could be the rationale for/against it? I'm not sure I understand the consequences of doing it so.
After learning a thing or two from the answers and comments, I've collected here a few examples :
http://rapidminer.com/the-core-of-rapidminer-is-open-source/ (note the angry comments on this one - but we're doing the opposite, from proprietary to open-core)
As a developer, I would use the product we are going to release it in personal projects, so I think it's useful. But I have been working on it and I have an obvious bias.
Also, most feedback I've seen basically says "you can try, but it won't work". See also http://blogs.gartner.com/brian_prentice/2010/03/31/open-core-the-emperors-new-clothes/
If someone is able to find a successful product doing open-core, I'd be grateful.