You can setup a secondary OU to to create new users for the new domain in and then assign a custom attribute to identify the new domain.
Then change the recipient policy to select users based on the custom attribute to make sure these users pickup the new domain name in their email addresses.
Depending on the number of users you have you can setup a one-to-one mailbox forward for all mail received in the second domain and create send as permissions for a user in the old domain on the new domains account.
This gives them the ability to select a secondary send as account when sending emails.
If this is not enough information to help you, please let me know and I'll expand, or if you have hundreds of users, then it may not be a workable solution.