You did not say what mail server is storing your emails. These days, it should be one of the IMAP servers - like Cyrus, Dovecot, Courier, ...
I personally like Cyrus IMAP. It supports this with relative ease:
Plus addressing - allows direct delivery to a particular mailbox (other than an INBOX). This is done via an address of the form: username+mailfolder@domain, which will deliver to the user's INBOX.mailfolder folder (or altnamespace equivalent). This submailbox must allow the posting user the 'p' right.
Adding 'p' right is important step - otherwise all mail (using + or not) will be delivered to username INBOX.
Note that you should use LMTP (local mail transport protocol) to deliver your mail from postfix to IMAP server and also need to configure postfix recipient_delimiter (or recipient_delimiters) as described here:
recipient_delimiter = +