Your question is perhaps not clear. However, if you publish the contents part wise in journal(s), there is absolutely no need ( and you cannot do also) to compile the published papers and republish them in the form of a book.

I have done that, twice, in two rather distinct fields. In both cases, I started by writing journal articles - two or three - and in each of the two cases I waited a couple of years, doing something else, after which I had a very clear view of the book structure. Since I had published the articles already, I could borrow some of my writing from the journals; that was a very big help. So in both cases I added more theory, numerical examples, and a rather substantial survey in each case.

On the latter - the survey was in each case a very well thought out one, in comparison to the modern-day typical rubbish of this variety, in which - typically you get a sentence followed by "see papers [56-76]". If you want to write a book that you want to be used well, you simply have to prepare the text of the book so that it follows a very well thought out thread; this is something that I find lacking these days. Also, as I mentioned above, you need to connect what you do with related past work - and not just with the lazy phrase "see [34-45]", but through a careful description of each work and how they relate to each. It may take a long time to compile such a survey, but you will have great use of it.

A lot of publishing authors do this; they publish individual articles in journals, then they put them all in a book-size manuscript, making the necessary changes and updates. As Michael suggested, you either wait for copyright to be automatically waived a couple of years after publication, or you might seek permission from the publisher. Usually, publishers won't say no since they had the privilege of publishing the original work, and made money out of it.

Thank you all so much! This has been very helpful!