You can use ROW_NUMBER() to achieve the desired results

SELECT*

FROM(

SELECTROW_NUMBER() OVER ( PARTITION BY Client.ID, Patient.SSN ORDER BY StartOfCare ) AS RN,

Client.ID, Client.ClientName, Patient.ClientID, Patient.SSN, Patient.StartOfCare, Patient.PrimDiag

FROMClient Client

INNER JOIN Patient Patient ON Client.ID = Patient.ClientID

WHEREPatient.RptYear = 2012 AND Patient.PrimDiag <> 'NULL' AND Patient.PrimDiag <> '' AND Patient.SSN <> ''

) P

WHEREP.RN > 1