Goodreads Librarians Group discussion
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Steinbeck - Is this a series?
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I would lean towards no, but I've never actually read any of them. (I know, I know. They're on my "someday" list!)

I did some googling and while I found multiple sites calling it a series, no one mentions anything in common other than them featuring migrant farm workers in Cali during the dust bowl.
I'd give it a few days to see if anyone else has more information. If there are no further replies by early next week, I think zapping the series would be fine.

https://www.goodreads.com/series/1987...
Wikipedia refers to it as the "Dust Bowl Trilogy" on Steinbeck's main bio but not on any of the individual book pages - and it's mentioned as a side remark, not in detail.
I've read only 2 of the 3 but I don't recall any overlapping characters or plots.