I am wondering where I might look to see what has been done in terms of Calculus of Functors for more general weak equivalences and Model Categories.

I am at least aware of some of the extended definitions of the main concepts in Calculus of Functors to weak equivalence such as homotopy limits, but I was wondering if a document existed that worked through the basic of COF in this setting.

I am aware also of Lurie's work here.(Thanks Harry for pointing this out.)

I appreciate your help.