Incompatible technical standards are one way of getting multiple primary keys, the other is to have organisations that cannot accept keys provided by other organisations. National administrations are particularly good at this, as acknowledging any other national organisation would be akin to admit that there are multiple countries on this planet.
The book Le musée du Silence has two ISBN codes: one for Canada, and one for the rest of the universe. The one used in Québec is 2-7609-2463-7 (978-2-7609-2463-5), and the one used elsewhere is 978-2-7427-5491-5. Notice that there is no common code between the two systems, we have true incompatibility.
It is interesting to see that this book published in 2005, two years before ISBN-13 became mandatory already uses the new system for Europe, but not for America.