So, how many addresses can a server have?

State?

If they are logging in at different times, their dynamic IP address has changed.  There are a couple of ways that this will happen.

When people were on almost exclusively on dialup, they had a time limit to be online.   Even if they had unlimited service.  I personally used to get disconnected after being online for 8 hours.  My internet would disconnect and when I reconnected I would have a new IP address. This happened every time you redialed to connect.   

 This can still happen even when you are using DSL. Your IP address will change on you when you lose a moment of connectivity.  Also there are those people who completely shut their DSL modem down every time they get off the computer.  Restarting their DSL will give them a new IP address. 

Now if they have a static IP address, I can't explain why it would ever change, because that would be a dedicated IP address on that account and there should be no other.

Also, if someone is on a smartphone that has WWW capabilities, you might see something like that more than a PC at home or work. I've found that with the local cable and DSL providers even shutting off your equipment and turning it back on won't always result in a new IP address. It just depends on how long your ISP's DHCP lease lasts (which is damn near impossible for a user to find out - unless you ask).

These two would know. :)

I travel a lot in the summer. Log on with my laptop or cell phone. May end up showing 5 different "states" during the day.

 I have a server in Florida that gives IPs from 3 different states because we set them up that way. All depends on the ISP you have.