Does the punctuation in the following sentence make sense?
John is popular among clients, as well as the management who have been very pleased with his work.
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Yes, it makes sense, but you need a second comma before who, because what follows is a supplementary, rather than an integrated, relative clause. That is to say, it provides additional information about the management, rather than defining them.
However, you might like to consider whether it would be clearer like this: