Official rules state that "you cannot be more on fire." Well...I think you can be.
If hurt by an elemental attack that does damage each round (such as fire, cold, acid, etc) you will take the initial damage. However, on the first attack a body part will be determined on which the damage is occurring. If damage is done on multiple parts of the body over multiple attacks then said damage will stack. However, damage to the same part of the body will not stack.
If a player is attacked by a fireball and it is determined that the attack hit the right arm, then the player will be taking 1d6 fire damage to that arm. On the next turn, if the player is attacked by another fireball and that attack hits the chest, then the player will begin taking 2d6 fire damage.