Is there a way to set up an Exchange mailbox to collect email "anonymously"?

What my company wants is for an email box to be set up so that when an email is sent to it, the From: field would be blanked out so that it would be anonymous. Is there any way to do this either through Exchange or third party software?

If you're using Exchange 2010 try the following in the Exchange Management Shell.

New-TransportRule -Name "Remove Header: From" -SentTo RecipientAlias -RemoveHeader "From"

This should create you a Hub Transport rule to remove the From header. All you need to do is change RecipientAlias to the actual alias of this anonymous receiving mailbox.