Claimed & received EIC already, but got Notice CP09 anyway

I filed a client's 1040 about three weeks ago, claiming the Earned Income Credit. The client has already received a refund of the amount expected.
Today the client got a Notice CP09 from the IRS, stating "You may be eligible for a refund of up to $5,751", which is more than what the client's actual refund was, based on income, two eligible children, etc. The notice is dated a few days in the future, so we don't know whether it was printed before the client's refund was issued.
What's going on here? Client is hoping for more money, but I'm positive that there is no more EIC coming. Is the IRS trying to complicate our customer service as revenge for Loving v. IRS? :-)
Lee
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Lee Choquette wrote:

This sounds like a generic letter that lists the maximum possible EITC amount one can get.
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Bingo?
The CP-09 is intended for taxpayers who have not claimed the EITC but may be eligible. What did your client do on his/her 2011 return?
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