We (publisher) have agreements with a number of other publishers to sell some of their books on consignments in certain regions (including via our international distributors).
We have never previously created DOIs for these books before, but since we assign them an ISBN under our publisher prefix when we register them (this is necessary to add them to our system and display them on our website), I figured it might be a good idea to start doing so, regardless of whether the original publisher has already given a title a DOI. That way, there’s a DOI leading to our website with our ISBN, and one leading to the original publisher’s website with their ISBN (if they’ve submitted one).
Based on this answer, I suppose one might consider it a sort of different format (even though it is really the same format, just sold by a different publisher). We certainly don’t want it to be a transfer of any DOI the original publication may have, since the original publisher still sells it.
A problem also occurs with titles that are part of series (or journals). Since these series belong to the original publisher, not us, attempts to submit metadata for ‘our version’ fail with an error that “The series with ISBN XXXXXXXX belongs to publisher 10.XXXX”. We can of course get around that by not including the series details, but that is definitely not in the spirit of DOI.
So is this actually a good idea? Or should we refrain from ‘double-indexing’ titles in this way? I suppose if the primary purpose of DOIs is to make it easier to reference books in a unique way that leads straight to the source, it doesn’t necessarily make sense, since citations should point to the original publisher.