According to Suffolk Manorial Families Thomas Chaplin of Blankney who died in 1748 was the son of John Chaplin of Tathwell and his second wife Frances Archer (the widow of Francis Rous of Rous Lench). Frances apparently left a PCC Will proven in 1719. Suffolk Manorial Families says to check Burkes Peerage for Thomas' descendants.
John Chaplin of Tathwell born 1657 was the son of Sir Francis Chaplin knight, citizen and clothmaker of the City of London and his wife Anne Hutt. Francis left a Will proven 1680 and Anne's was proven in 1692.
Francis Chaplin was the son of Robert Chaplin of Bury St Edmunds, woollen draper, whose Archdeaconry of Sudbury Will was proven Feb 1643/4. His wife was Elizabeth Asty and they married 1627 at Bury St Mary.
Robert was baptised at Semer, Suffolk, in 1602, his mother it appears died in or just after childbirth. Robert's parents being William Chaplin of Semer and his first wife Agnes Holborough who married at Bulmer, Essex, in 1581. William died in 1629 and left a PCC Will, in which he mentons three siblings Thomas Chaplin, Joan Ballard and Clement Chaplin. My interest in that Chaplin family is with Clement Chaplin of Action, Suffolk, Wiliam's brother.
As I said I've not confirmed all of this information, only for now to William Chaplin and his wives Agnes and Anne. The pedigree suggests he left a Will when he died in 1629 but I've no record of that one.
Hope this helps. Obviously needs some checking.
The Chaplins in Suffolk can be very confusing with similarly named children and in neighbouring parishes. I have seen a few inaccurate family trees about because people haven't checked Wills and parish register entries accurately.
I await the parish registers finally appearing on Ancestry in probably a couple of years.