Is it possible to host multiple domains without using fqdnaliases?

[Kelly Peterson <kellyp@compusmart.ab.ca>]

For example, we want to be able to have user1@domainone.com and
user1@domaintwo.com but we don't want to have to use fqdnaliases.  More
specifically, we don't want to tell users that" your email address is
user1@domaintwo.com but when you check your mail use
user1.domaintwo@domaintwo.com as your pop account.

Forgive me if I am not clear in what I am asking for.  I don't know the
terminology.