Sinai was never the Pagets' main house, these being the manor in Burton, their country house at Beaudesert and eventually their grand new home in Anglesey, Plas Newydd, designed in the 18th century by James Wyatt. So Sinai was used as a hunting lodge and later as a farm. To make the house more grand and presumably to provide accommodation suited to the family's grand visitors (one of whom was Elizabeth's Earl of Essex, recorded as shooting deer in the park), the Pagets had the central section built in 1605, to complete the building we see today.
In the 1700s there was more building work with the originals of the Tudor-style chimneys being erected, again to make the house more grand.
Also from this period is what was then a very fashionable plunge pool, built in the grounds, using as its source the Chalybeate well below the house. The 1732 bridge over the moat is also an aggrandisement of an earlier bridge, originally one of four similar access points and the site of a 'skirmish' between the Paget men and the Bagots of neighbouring Blithfield during the English Civil War!
All this building activity during the 18th and early 19th centuries may have been to do with Sinai's increasingly well known tenants. While the architect, James Wyatt, was being commissioned by the Pagets to build Plas Newydd, his brother William was the tenant of Sinai.