After writing a series of comments related to your question I thought a bit more about it and came to the conclusion that capitalization is optional in these cases, depending on the context.
(1) As MikeJRamsey56 rightly noted in comments, the words 'Ocean' and 'County' as used in these examples are not really 'common nouns' as OP calls them, but (I should think) part of 'proper nouns' as in 'Pacific Ocean' and 'Columbia County' -- considered as such, capitalization of the part of a proper noun coming at the end of a list of proper nouns would be a good option:
Bob: Did you say you swam in the Pacific Ocean or the Atlantic Ocean?
Mike: In fact I swam in the Pacific, Atlantic and Arctic Oceans.
Bob: And the Arctic Ocean? Well, I just hope none of your toes got frozen off, nor any other appendages. BTW where had you worked before you started here?
Mike: Fulton County, Columbia County and Cook County...
Bob: You had better say Fulton, Columbia and Cook Counties, because the boss is a senior member at EL and U!
(2) However you can also legitimately use 'ocean' and 'county' as generic common nouns whose specific names then become identifying adjectives here.
Bob: Which oceans did you swim in?
Mike: The Pacific, Atlantic and Arctic oceans.
Bob: Which counties give special exemption on residential tax for mobile homes?
Mike: Fulton, Columbia and Cook counties, I think.
A note on style: The senior member Sven Yargs has observed in comments regarding style guides that both Chicago and AP endorse "Pacific, Atlantic[,] and Arctic oceans," without admitting any exceptions. I am sure all style guides would advise you to be consistent in either case.