For your example query, the only possible value greater than 2 and less than 4 is 3, so we simplify:
GROUP BY meetingID
HAVING COUNT(caseID) = 3
In your general case:
GROUP BY meetingID
HAVING COUNT(caseID) > x AND COUNT(caseID) < 7
Or (possibly easier to read?),
GROUP BY meetingID
HAVING COUNT(caseID) BETWEEN x+1 AND 6