Is it possible to make Messages on the iPhone and Messages on the Mac interchangeable in the same way that Calendar on the iPhone and Calendar on the Mac are interchangeable? If so, how?

JoBoy,

See if this Support page, helps:
Add or remove your phone number in iMessage or FaceTime on your iPad, iPod touch, or Mac.

Thank you. After playing with it for a while, I've decided it is not exactly what I had in mind. I appreciate the reference very much.

Does anything in this search results page look like what you're looking for?

Thank you. I've decided to not try to do what I set out to do. It just isn't worth the effort. Your assist was very helpful.