I'm not aware of any specific examples, but yes it's possible.
For your question about ISBNs, it's important to understand that the ISBN is an identifier to the publishing of the book (roughly the FRBR Manifestation). Reprintings don't typically get a new ISBN number, but changes in packaging (hardback vs. paperback vs. large print hardback) would.
(FRBR, the Functional Requirements for Bibliographic Records, deals with the issue that "book" has different meanings, and so it defines "Work" to be the overall creative work, which is realized through an "Expression" and embodied in a "Manifestion" and exemplified in an "Item". So we have "The Bible" vs. "The King James Bible" vs. "ISBN ...." vs. "The dog eared bible that my aunt gave me". Of course that example neglects that the bible is actually a collection of Works not a single Work, but it should get the point across)
Occassionally reprintings will get a new ISBN, but it's up to the publisher to decide. ("Now with a new foreword by the Author!", "20th Anniversary Edition!" are more likely to get a new ISBN than simply '7th printing')
New editions (a new FRBR Expression or a new FRBR Work, depending on the extent of the changes) should always get a new ISBN, as the publisher wants to sell people the new book and make sure they understand that it's a new book.
So, would an old ISBN be sold under a new ISBN?
I've seen it happen, in the case of collections -- a box set is composed of the original releases, each with their original ISBN, but the box has a new ISBN on it.
I don't know if they qualify as 'series' but in terms of 'sets' or 'collections', I could see publishers selling a book individually, then as a trilogy, then as a 'complete series' later, and possibly later as a 'complete works of (author)'.
In academic publishing, you might have a series of chapters collected into a book, and some of those chapters appearing again in some other book.
I could see something like your example if you were to have a publisher like Time Life have a book on World War 2 Aircraft, and then have series on both "World War 2" and on "Military Aircraft", and recycling much of the content. But the publisher wants you to buy both copies, so they'd likely rework the content to make it look like a totally new book.
Another possibility might be in cookbooks ... if you had a 'Christmas Cookies of Italy' book, it could be sold in a 'Christmas Cookies of Europe' set or as a 'Cookies of Italy' set. (but do they count as 'series'? I don't know).
The only case that I can think of where I would say that they definately qualify as part of multiple "series" would be "cross-over" type stories in fiction, where characters from more than one series are present. This often happens in comic books, and may happen in cartoons or tv shows, but the "cross-over" story may be told across multiple series (eg, Marvel's Onslaught Saga) or there might be slight title variations so they're not technically part of each "series" (eg, Marvel's Civil War), or it might be a special, unique publication (that may end up as a new series, like DC's World Without Grownups was the lead in to Young Justice)
(Note that 'crossover' when talking about books is about appeal, not content; it usually means books that are liked by both teens and adults. I'm not using that sense of it)
More common seems to be there being a "special" edition or a separate series for the cross over (eg, JLA or Avengers for comic books, but there were Nancy Drew / Hardy Boys books and a TV show, and The Jimmy/Timmy Power Hour and Rugrats go Wild on Nickelodeon). In these cases, they might fit between specific issues/episodes of multiple series, but they're not exactly a member of those series.
Or you have a couple of characters from one series show up in another (which may just be an allusion or easter egg, like frequently happens in Stephen King's Dark Tower series or most works by Neil Gaiman).
Official collaborations are more likely to happen in series by the same author/creator (eg, X-Files wrapped up some plot points from Chris Carter's canceled TV series Millennium; The TV show Archer had the titular character lose his memory and appear in Bob's Burgers (voiced by the same actor)). (it's huge for TV shows ... not even counting The Simpsons. See http://www.poobala.com/crossoverlist.html.)
... but I don't know that any of them would really match what I think you're asking.