Which one of these two statements is correct?
Our staff do ...
Our staff does ...
And is staffs ever correct?
In British English, one can say "our staff do", because they use plural verbal agreement to emphasize when an entity is made up of a group of people, whether this entity itself is marked as plural or not. This is also true of companies, bands, sports teams and other things which are commonly used in plural forms as well as singular forms. The verbs are usually plural for one band or many bands ("Many bands play at the festival" as well as "Radiohead are a band").
In American English, one says "our staff does", because in our grammar, we are not concerning ourselves with whether an entity is made up of many people or not. Since staff is singular, we treat it grammatically as singular. It is no different for us than a stick-staff in terms of grammar.
Staff (when meaning a group of employees) is a collective noun with no plural. So, it's "our staff do good work".
When referring to a group of sticks, it's "staffs" in American English and "staffs" or "staves" everywhere else.
I disagree with Kosmonaut. In BrE, staff is used as both a singular and a plural for purposes of agreement, although plural is certainly more popular.
Here are some examples with singular (from the Oxford English Corpus):
EDITED: Removed useless example.
With regard to the question "is staffs ever correct?" I note that a Google Books search for the phrase "merged their staffs" returns nine relevant unique matches, ranging from in year of publication from 1951 to 2014. Here are three typical examples. From Virginia Department of Welfare and Institutions, The Welfare Worker (1951):
From Douglas Fox, The New Urban Politics: Cities and the Federal Government (1972) [combined snippets]:
From Alan Kraut & Deborah Kraut, Covenant of Care: Newark Beth Israel and the Jewish Hospital in America (2006):
Google Books search results indicate indicate that in U.S. English "merged their staffs" is much more common than "merged their staff," which yields a single match. From Damien Broderick, The Spike: How Our Lives Are Being Transformed By Rapidly Advancing Technologies (2002):
This is consistent with my experience. When the publisher of the computer magazine I worked on decide to combine that magazine's staff with the staff of another computer magazine that the publisher owned, the process was referred to as "merging staffs." At any rate, that situation is one in which staffs as the plural of staff appears to be correct in the sense of "in common U.S. usage."
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