Are this sentence’s needs being met?

A colleague just asked about a sentence similar to the following:

Provided that each member of the faculty club’s basic needs is met along with a comfortable free wine allotment, each professor will remain suitably compliant to expectations.

He question was whether it should be is met or are met; she was leaning towards is because it’s each member.

How do you sort out questions of conjugation? Find the head of the noun phrase that’s the subject of the sentence. What’s the head noun here? Is it member? Only if the faculty club’s basic needs is what it’s a member of. But I rather suspect that it’s actually talking about the basic needs of each member of the human family – in other words, the ‘s on club’s actually applies to the whole phrase each member of the faculty club… which makes that phrase a modifier of needs. And so “needs” is the head noun, the one that the verb conjugates to. (Anything that has a possessive, and anything that is the complement of a preposition – e.g., of the faculty club – is a modifier.)

The skeleton is in fact Provided that … needs … are met …, each … will remain … compliant. The rest is modifiers. And yes, it’s are: it’s the needs that are being met, not each member that is being met.

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