I spent probably too much time overthinking this sentence while proofing an article this morning:
If things just don’t work out for either party, your firm and the agency each have a way to exit the relationship.
The word each in that sentence made me consider whether the verb should have been has instead of have. Each calls for a singular verb. But in this case, each appears after a plural subject, your firm and the agency, so the choice is have.
I could have marked each for deletion without affecting the meaning and taking each out in my head helped me discern that the plural verb was OK. I didn’t mark that deletion because on a proof I try hard to correct only errors.
Later, as I wrote this post, I turned to The Gregg Reference Manual, 10th edition, and found this at 1009c: “When each follows a plural subject, keep the verb plural. In that position, each has no effect on the number of the verb. To test the correctness of such sentences, mentally omit each.” (I must say for the umpteenth time: Gregg is an invaluable resource.)
If the sentence were instead:
If things just don’t work out for either your firm or the agency, each of you has/have a way to exit the relationship.
The traditional choice is a singular verb (has) to agree with each, but a writer might choose the plural verb (have) because the reference seems to be to two things: your firm and the agency. Or, perhaps, the writer might choose have to go with you. As a copy editor, though, I can confidently choose the singular verb.
Or if the sentence were this:
If things just don’t work out, each firm and agency has/have a way to exit the relationship.
We should choose has when each precedes two or more nouns (firm and agency) joined by and. That goes for every, many a, and many an, too, as Gregg points out in 1009b.