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Which is correct (and have you got a source)?

"Animals store vitamin C in their liver."

"Animals store vitamin C in their livers."

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    This is not related to prepositional phrases, but to the number of ownees by a number of owners. If the livers in question are in the object position, the exact same problem appears: “Alcoholics tend to damage their liver(s)”. – Janus Bahs Jacquet Sep 18 '14 at 21:40
  • An animal stores vitamin C in its liver. – Gary's Student Sep 18 '14 at 21:54
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    You're dealing with Generic noun phrases here. The plural of Animals is not a real plural, but a plural generic; it doesn't individuate -- i.e, you can't depend on one liver per animal -- since it's not referential, but generic. – John Lawler Sep 19 '14 at 00:27
  • @John: even if it was not generic but referential, you still couldn't differentiate. "The team members are putting on their uniforms and their shoes" ... each member has one uniform and two shoes, but there is no way to tell that from context; you must use the plural here. – Peter Shor Sep 22 '14 at 14:56
  • Nah, if the animal is generic, so is their liver. So any Vitamin C in a generic animal can be stored in the generic liver. No plural necessary; with generics, the plural marker doesn't mean plurality as such. – John Lawler Sep 22 '14 at 15:42

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I don't have a source, but see below, all four are valid sentences that mean something different.

The attendant is loading things in my car.

I have one car, and an attendant is loading things into it.

The attendant is loading things in my cars.

I have more than one car, and a single attendent is loading things in each of them.

The attendants are loading things in my car.

I have one car, and multiple attendants are loading things into it. I'm getting great service here.

The attendants are loading things in my cars.

I have multiple cars, and multiple attendants are loading things into each of them. I must be rich or something. :)

The lines can be blurred with indefinte nouns but the rules still work the same.

Regarding your original example, the second sentence:

Animals store vitamin C in their livers

could be construed as saying the animals you are talking about have more than one liver, though a native English speaker is likely to understand you mean one animal = one liver (because that's how things are usually) unless the context was different.

Really, to be clear, you want to say:

Each animal stores vitamin C in its liver

or

Animals store vitamin C in the liver