Hi all. I can't figure this one out. Is it possible?

I've got a query I use to find duplicate firstname/lastname pairs in my database of contacts:

Code:
SELECT FirstName,LastName,COUNT(*) as cnt
FROM a_contacts
WHERE FirstName != '' AND LastName !=''		
GROUP BY FirstName,LastName 
HAVING cnt>1 
ORDER BY cnt DESC, LastName, FirstName
It works fine, but I want to extend it a bit. I want to find the groups of duplicately named people where either ONE (or more) of them have a particular GroupID.

If I do this...

Code:
SELECT FirstName,LastName,COUNT(*) as cnt
FROM a_contacts
WHERE (FirstName != '' AND LastName !='') AND (GroupID=1)			
GROUP BY FirstName,LastName 
HAVING cnt>1 
ORDER BY cnt DESC, LastName, FirstName
...I get the duplicates where ALL the people have the GroupID of 1. I want to write the query so that it catches all of the duplicate names as long as at least ONE has the GroupID but not necessarily ALL.

I can't imagine how to do it. ??
I'm in mysql 5.0 btw.