Return Entire Row which has the first Max Value in One Field
This is a simple task for a ranking function:

WITH cte AS
 (
   SELECT  prodMPEntity, 
       prodMPLiquid,
       prodMPNormMonth,
       prodMPProdDate,
       ROW_NUMBER() -- assign a rank based on your description
       OVER (PARTITION BY prodMPEntity
             ORDER BY prodMPLiquid DESC, prodMPProdDate) AS rn
       FROM    dbo.prodMPRunningTotals
       WHERE        (prodMPNormMonth &lt;= 6)
 )
SELECT   prodMPEntity, 
    prodMPLiquid,
    prodMPNormMonth,
    prodMPProdDate
FROM cte
WHERE rn = 1 -- return the row which is ranked 1st