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I'm a PhD student in the field of operations management. I've just finished writing a chapter in a handbook and am thinking about rewriting it into a publishable paper.
How much of the content can be the same and what else do I need to consider - such as empirical data, new conceptual development, etc.?
There is absolutely nothing wrong with using research you've already published, whether in a book chapter or any other format, as a basis for further research that could lead to a new publication. However, it sounds to me like the way you are approaching this is a classic example of putting the cart before the horse.
Your goal should be to do new research that contributes something to your area, not to artificially boost your publication list by rehashing old material, which as I said in the comments is the definition of self-plagiarism. Once you have found something new to say beyond what you already wrote about in your book chapter, it will become naturally apparent to you when it makes sense to publish your findings, so the question you are asking here will likely never need to be asked. The point is that publishing is merely the last step of the process of doing research, and in some sense the least important step. It is the means to the end of communicating your research results, not the end unto itself.
As for the practical question of how much material from the book chapter you can include in a new publication, there are different schools of thought on this, with some people viewing any inclusion of substantially similar text from earlier publications, especially without an explicit citation and mention of the similarities, quite negatively. I advise you to consult your advisor or a senior colleague who is familiar with the norms in your area about such things.
I strongly believe, the best practice is to treat your published book chapter (or another published work by yourself) as if it was written by someone else. Use it in your new contribution to the same extent as you would reuse a work published by your colleague. So basically you should explicitly cite the source every time when you use any of your prior work in a new paper. ("HSC (2016) wrote so and so..." [this is the only permissible option if you anonymize your contribution for a double-blind peer review]; "as proposed elsewhere by the present author (HSC 2016)..."; "I earlier proposed (HSC 2016)..." etc..). Even if your particular discipline may take a different stance on self-plagiarism as suggested in other comments and replies, it does not make it a good thing. (Consider also that if your paper is subject to double-blind peer review, the reviewer will make no difference between self-plagiarism and plagiarism from another author).
If your question was how to turn an article originally intended to be published as a book chapter (but not published at all) into a conference paper, that would make some reasonable discussions based on your field. Because this will lead us into discussing how book chapters differ from the conference papers or journal articles.
But your case is different. It has already been published as the book chapter! This makes the answer to the question flat and simple.
"How to turn a book chapter into a publishable paper?" "You cannot turn an existing book chapter into a publishable paper".
If you must make a new paper on the same topic, it is going to be an entirely new one (citing previous work, as mentioned already by @greenb). It is not "turning a book chapter" as a new paper - like old wine in a new bottle.
@Dan Romik has answered in detail to your other sub questions.
