The US Postal System actually uses a full 11 digit number to identify a "Delivery Point". The "+4" after a zip code is basically a subroute within that zip code, but there are two numbers after that you don't really see that will identify the full delivery point, which is basically a mailbox. The USPS tracks a number of things at this delivery point level, including whether a secondary address is needed, if they are currently delivering to that address, or if service is temporarily suspended (potentially due to a natural disaster or road outage in the case of a more remote rural address).
I'd really love to see if just a full 11 digit number is enough to get mail delivered to my house. I guess I could try, as it's easier than you'd think to find out your code