[CentOS] Running Apache sites as separate users

I had a recent request to improve security on my web servers by having each
website use a different user to run the hosting service.  So
example1.comhas it's own Apache instance running as apache1 and then
example2.com has its own instance of Apache as apache2.  Is this even
possible or realistic?  I understand the idea of how that would be secure,
much like creating a virtual machine to segregate services.  The only way I
can think how this is done is to chroot each website.  What makes this
request even stranger is that each website will be managed by the same CMS
and code base.  So with that being the case, I don't see how this is
possible.  Any ideas or insight are very welcome.

Thanks
- Trey