Richard More had few descendants, with only his daughter Susanna (with her marriage Samuel Dutch) having descendants.
Are you a member of the Mayflower Society? In the Mayflower Society, I'm sure that those who claim descendancy from Richard More are in rare company compared to others who claim descendancy from other Mayflower persons.
My descendancy from Richard More is as follows: Susanna More & Samuel Dutch Susanna Dutch & Benjamin Knowlton Susannah Knowlton & Josiah Dodge Josiah Dodge & Hannah Conant Mary/Polly Dodge & Cyrus Warner Miriam/Mary Warner & Foster Ketcham (desc. of Isaac Allerton) Milan Ketcham & Sarah Harper Ransom E. Ketcham & Nancy Jane Campbell Fay S. Ketcham & Halleck F. Gray (desc. of John Howland & his father-in-law John Tilley) Ruby J. Gray & Alton H. Rogers
The Jane Pemberton & Sir Thomas More situation might certainly warrant further study. Thomas More was born in London, a son of a judge John More. He has always been a fascinating person in history and his character is in any film about Henry VIII as a man who died rather than compromise his principles.
David Lindsay in his book references his visit with Donald F. Harris in Shropshire. Mr Harris has provided much on Richard More for U.S. genealogical publications over the years and when I contacted him a few years ago, he kindly provided me with several documents that helped me with Richard More's Shropshire ancestry. I can share these with interested persons.
With Richard More being the only person on the Mayflower with proven royal ancestry, that has kept me busy enough this past year or so. His mother Katherine could claim as ancestors a great many of the royal and historic persons of the Middle Ages - Saxon, English, Welsh, Scots, French & Castile/Leon/Navarre (modern Spain) (and many other places) royalty and many famous/historic persons that range from Sir William Marshal, "The Greatest Knight" (Richard was descended from all 5 of his daughters!) to the legendary Castillian nobleman, El Cid. This in addition to having had ancestors who were barons at the Magna Carta in 1215 and were commanders at the Battle of Hastings in 1066.
Recent books by Douglas Richardson, Plantagenet Ancestry and Magna Carta Ancestry detail Richard's royal ancestry, as do many other books.
I can detail more of this to your e-mail address if you are interested. I have numerous files written narrative-style (not Ged-coms) on most his ancestors and can provide a list of these as an e-mail attachment if you can open Microsoft Works.
Let me know if you are interested. Regards Alton Rogers