Email addresses need to be unique - only one recipient can have a particular
email address.

One way to accomplish the desired result - set up another mailbox (or
distribution group, if you want to distribute incoming email to that address
to all users). Make sure this user gets the email address (as primary SMTP
address) you want to send out as.

Add everyone who needs to send as this user to a group.
Assign "Send As" permissions to the group.
When users want to send mail as this new user (with the desired email
address), have them add the new user's address/name in the From: field in
Outlook.

(Alternatively, you can have them use Outlook Express to send these
messages).