How can I cite multiple chapters from the same book? Do I have to use separate reference numbers, if they are by different authors?
Since the Uniform Requirements for Manuscripts Submitted to Biomedical Journals (commonly called the Vancouver system) is also widely referred to as an Author-Number system, it will necessary to have a number for each author of a multi-chapter compilation (and more than one number for an author who produced two or more chapters).
Logically the treatment of a book to which several authors have made distinctly identified contributions should be the same as that of articles collected in a journal.
If I understand your question correctly, you want to cite from one book which is written by several authors.
Even if you know which paragraph was written by which author and you cite different authors it is still one book. The idea of listing the sources is, that a reader can order these books and look up the source.
Now, if you have six different reference numbers, because you cite six different authors of the same book, the reader will be very puzzled why he has ordered the same book six times.
Ok, probably he will figure out that theses references refer to the same book, but there is no need to puzzle him. It's one book, so use one reference number.
When you want to show that you cite different authors, you can do that in your text. Like "Mr A. Smith has written blablabla" or putting the name in parentheses after the citation or whatever. But you do not need to do that. Referencing the source in the usual way is enough.