When the subject of the sentence is plural, should the nouns that follow agree with the subject's plurality?

Question

For example:

In this stage, writers review and amend their paper to better articulate their intended message.

Should the terms "paper" and "message" remain the same or become plural?

Thank you in advance!

Answer 1

Yes, they should, or must, unless the paper has more than one author working in collaboration.

Answer 2

I thought so. Thank you again.

Answer 3

You are quite welcome. :)