I have a client that is going through rebranding process.  They like to do the following:

 

(1) Change domain name 
(2) Receive email from old domain and new domain
(3) Allow users to access their old email, still receive emails from old domain but from their new domain too
(4) Have all outgoing emails come from their new domain

 

Once I setup the new domain mx record.  Do I just add a domain alias for the new name on their existing domain? What about #4?

 

What's the best way to accomplish this?  Thanks!