Anyone descending from a Partridge have DNA Test Results on 23 and Me...?

A possible "cousin" has made contact and is thought by 23 and Me to be my 2nd to 3rd cousin with 2.49% genomes shared in 9 segments.  This individual doesn't know who her father is and her mother is adopted.  All three of our children have had their DNA tested by 23 and Me.   This opens up a lot of possibilities in analyzing relationships. We're now wondering if we can find any more relatives who have had their DNA tested at 23 and Me.  We have already connected with other relatives and since her haplogroup is different, this probably puts them out of the question for this young woman. We'd like to compare results and either negate or accept lines as possibilities for her and to bring up more possibilities in our own make up.  We have narrowed it down to Partridge.  My great grandmother was Sally Partridge McKay.  Sally's father was Daniel Woodward Partridge and her grandfather was Asa Partridge (1759-1845).  Lineage further back may be:  John Partridge IX (1716-1806) > Samuel Partridge III (1687-1744) > John Partridge V (1657-1731).  Anyone related to this line of Partridge's...?

Thanks in advance,

Nancy Cluff Siders