Does catching on fire stack if a character catches on fire again while still burning?

The effect catching on fire is unclear on if it can happen multiple times to a character. For example, the spell Fires of Purity (Complete Divine p.165) states:

Any creature taking fire damage from fires of purity must succeed on a reflex save or catch fire. Creatures on fire burn for 1d4 rounds and take 1d6 points of fire damage each round, unless they succeed on Reflex saves (at the spell’s DC) in subsequent rounds or douse themselves in water (see Catching on Fire, page 303 of the Dungeon Master’s Guide).

So for a hypothetical situation, a dual-wielding fighter makes 5 attacks against a creature and hits all 5. The target must make 5 Reflex saves, and they fail 3 of them. Which scenario happens:

Scenario A: Max Damage

  1. The creature takes 3d6 “catching on fire” damage the first round from the initial ignitions
  2. The creature takes up to 3d6 fire damage for the next 1d4 rounds (1d6 fire damage for 1d4 rounds for each of the 3 attacks)

Scenario B: Medium Damage

  1. The creature takes 3d6 first-round catching on fire for the 3 times it caught on fire
  2. The creature takes 1d6 damage each additional round for the maximum number of rounds equal to the highest of its three 1d4 round duration rolls

Scenario C: Least Damage

  1. The creature takes 1d6 first-round damage, with no additional damage since it’s already on fire
  2. The creature takes 1d6 damage each additional round for the highest number of rounds from its three 1d4 round rolls

Damaging spells stack, per the discussion in this question, but this isn’t a spell. This is effectively a non-magical effect that boils down to “does a character who continues to be exposed to an effect that catches one on fire get more on fire.”