Hi Mich,
have you looked in the Norfolk Transcription Archives ??
http://www.genealogy.doun.org/transcriptions/search.phpThere are two PLUMPTON baptisms there in Attleborough.
They very likely link up to yours, as it's not that common a name.
From the dates given, Father Nathaniel could be William's brother ?
Wayland District, Attleborough
1770 PLUMPTON, Nathaniel, Parents Nathaniel & Lucy
1772 PLUMPTON, John, Parents Nathaniel & Lucy
Good luck,
Bob