You can do something similar with Gmail - if your email is matt@gmail.com you can receive to Matt+1@gmail.com, matt+2 etc.
Although some websites reject this format.
IMNSHO: sysadmins who do not know that the local part of an email address is not of their concern (as long as it complies to RFC 822++), are not worth their money. And web designers? Don't get me started on that topic ;-0
Edit: ok, they even allow "." and "-" in local parts.