The Copyeditor’s Handbook author Amy Einsohn offers a clear and simple rule for one of the cases in which a comma is not appropriate:
Do not insert a comma between a subject and the second member of a compound predicate.
An example follows.
They spent every cent that came in, and piled up hefty credit card debt on top of it.
The compound predicate is “spent every cent” and “piled up hefty credit card debt.” It should read like this:
They spent every cent that came in and piled up hefty credit card debt on top of it.
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