WIlliam Mead, Pleasant Satterthwaite (Mead)'s father should not (I believe)be confused with a WIlliam Mead who was of Virginia
Here are notes on WIlliam, father of Pleasant:
About Mead, William, son of Richard
"Baptised at Soulbury, Bucks on 14th November 1627. Went to London as a young man and entered into prosperous business as linen draper in Fenchurch Street. Admitted to the freedom of the Merchant Taylors Company on 9 Jan 1655 or 1656 by patrimony in virtue of his fathers membership. Admitted to the livery in 1658. Acted as Master in 1706. Lived at a house in Highgate. Captain in the London Trained Bands, a military body now represented by the Honourable Artillary Company. Joined the Society of Friends before 1670 and held a leading position among them. Came to America with William Penn, founding father of Pennsylvania and the American Quakers. Was arrested with Penn for preaching in the street. Purchased the estate of Goosehays about 1684, which was about three miles from Romford, Essex. Died there at Goosehays. Buried at Friends Cemetery, Barking."
This, in itself, doesn't prove parentage yet: We have WIlliam in America with Penn.
We also have WIlliam married, it is said not proven, to Sarah Fell, daughter of the famous Quaker Margaret Fell.