I am looking at buying a 2016 F-type R (10,000 miles) which was sold last year as a jaguar CPO vehicle. Does that extended warranty carry over to the next owner or not?

 

Yes, the warranty is transferable.

 

Yes, the extended warranty may be transferred if the seller elect to do so. I just bought an extended warranty for my 2016 F-type R and because if cost right at $4500 for 5 years/50K miles. If the buyer wants to pay less for the car my plan is to reduce the prices and sell back what's left on the warranty to Jaguar. Additionally, the extended warranties is bumper to bumper but when you buy the warranty you choose the deductible $500 or $250.

 

You are speaking, I think, about a different sort of warranty, or perhaps the CPO warranty provisions differ in different markets.
In Canada, if you buy a Jaguar with a CPO warranty (that is, an official Jaguar, not third party, warranty) from a dealer there is no deductible portion for repairs done at any Jaguar dealer. The warranty covers stated items (an enormous number of items covering the power train, electrical and other systems) exactly as the original new-car warranty does. If you, as the owner who bought the CPO car decide to sell it, then the warranty transfers to the subsequent owner, your buyer, under the same conditions and lasts until the warranty period expires.