My question may sound weird and I have no deep motivation behind it other than curiosity.
As is well-known, quasi-reflexive spaces have the Radon-Nikodym property hence their balls have lots of extreme points (they even have the so-called Krein-Milman property). However, can one give me an example of a quasi-reflexive space which is not isometric to a dual space? Of course, every quasireflexive space is isomorphic to a dual space.
I suspect that a clever renorming of the James space should do the job.