Carl is correct :) You can have more than 3 messages if you have the Premium voicemail or iPhone visual voicemail. These are included in a value pack that you can add to your plan.
If you have the mini voicemail which is the standard version included in all our plans, it can carry up to 3 messages at a time. To get more, you'll have to delete your messages to make room or add the value pack to your plan :)
Hope this helps!