You can be asleep, poisoned and burned at the same time, but if you then get paralyzed it replaces asleep. Think of it this way, there are three effects that require you to turn the Pokemon card to indicate the effect: asleep, confused and paralyzed. Since you can only have the card turned one of those three ways at any given time, you can only have one of those effects apply at a time. Those three replace each other.
BDS