Regret I cannot help you on this one. Only Richard's daughter Susanna More (married Samuel Dutch) has descendants who are alive today.
The More name is probably more English than other British or Irish - Richard was from Shropshire where his family's roots can be traced to the 12th century. In the medieval era and later there are many famous English persons with the More surname. A famous More in British history: http://en.wikipedia.org/wiki/Sir_Thomas_Morehttp://en.wikipedia.org/wiki/Sir_Thomas_More and other Mores: http://en.wikipedia.org/wiki/More_(surnamehttp://en.wikipedia.org/wiki/More_(surname)
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Sorry I could not provide more assistance. Good luck.