Burke in their 107 edition of their Peerage and Baronetage, pub 2003, give nine further generations of Blennerhassetts before this Robert.  Several of them are reported to have been MPs, so can be checked.  A nice little research project!

Additionally, Bill Jehan’s excellent study of all Blennerhassett families is thoroughly to be recommended:

http://www.blennerhassettfamilytree.com/