Will an Insurance Co. that has totaled your car give you extra cash for recent replacement parts in addition to the cash value?

No, unfortunately. For regular maintenance parts and labor no, however, if you've recently had work done that goes beyond normal maintenance and replacements, then it is possible. For instance, replacing worn tires would not qualify, but payment for overhauling an engine might. It also depends on your state statues and the Wording in your insurance contract.