@jsghagan – I am wondering still what you need to do this for. Do you need to retire olddomain.com and replace it with newdomain.com? You can change the domain that WordPress runs on. (You can’t map the domain for Site 1; you can completely replace the domain.) Changing that would be related to the process for moving WordPress single-site to a different domain name, except needs to check for olddomain.com in the additional tables for multi-site. Moving multi-site from development server to production server would require the identical process, if this is what you want.
I’ve never documented the steps for this. Somewhere I have notes which search/replace plugin I used. It would have to know about WordPress “serialized data” and multi-site tables.
Step 1, obviously, is Backup Your Data!
Step 2, backup again, to a different file name.
Step 3, I’ve heard prayer is always good.
Step 4, would you let us know what works, if this is even what you’re looking for?