Italian translation: conti del cliente/conti della clientela
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I feel I must ask both askers and answerers to look closely when replying:
Explanation: in English an apostrophe makes all the difference.
In the text attached by John, he wrote "customer's accounts" - that is several accounts that belong to one customer (conti del cliente).
If he had written "customers' accounts" or "customer accounts" then it is indeed plural for both (conti dei clienti/della clientela).