Using "staffs" to refer to people

This is a sentence in a book by Rudy Giuliani.

I could ensure my deputies and commissioners were working off the same page and could carry a coherent message back to their staffs.

Isn't staff a mass noun with no plural when referring to people?

Presumably Rudy Giuliani meant that each of his deputies and commissioners could carry a message to his or her staff.

This means several staffs

Yes, Staff is already plural. It refers to the people working for someone.

However, there are cases where it makes sense to use a plural form of a quantity noun. Chiefly this occurs in the cases where there are multiple different and distinct groups of the objects in question. This could well be argued to be the case where you are talking about the staffs of several different people. (I do so find myself wanting to say staves here. :-) )

Another good example shows up with the accepted answer for a recent question here: What is the plural of ivy?