The game doesn't say if a creature can be on fire more than once
To be clear, the game doesn't say, "A creature that's already on fire is not at risk of catching fire again." Of course, neither does the game say, "A paralyzed creature can't be paralyzed," nor does the game say, "A dead creature can't be killed." Really, by necessity, the game doesn't say a lot more than it does say. Filling in these gaps is part of what a Dungeon Master is for.
However, the Dungeon Master's Guide on Heat Dangers on Catching on Fire, in part, says
Characters at risk of catching fire are allowed a DC 15 Reflex save to avoid this fate. If a character’s clothes or hair catch fire, he takes 1d6 points of damage immediately. In each subsequent round, the burning character must make another Reflex saving throw. Failure means he takes another 1d6 points of damage that round. Success means that the fire has gone out. (That is, once he succeeds on his saving throw, he’s no longer on fire.) (303–4 and emphasis mine)
To this reader, a creature is not "at risk of catching fire" if a creature is already on fire, in the same way that a paralyzed creature isn't at risk of being made more paralyzed, a prone creature isn't at risk of being rendered prone, and a dead creature isn't at risk of being made even more dead. This reader freely admits that this is a legally precarious position to stake out, but this reader views the game as essentially saying that on fire is not a dial but a switch like a nonescalating condition. (To corroborate this slightly, like the Dungeon Master's Guide, the Rules Compendium uses the at risk language in its discussions of catching on fire (48, 104).)
On the rarity of catching on fire at all (much less multiple times)
No Player's Handbook equipment or spells cause a creature to catch on fire—not even alchemist's fire (flask) (Player's Handbook 128) (20 gp; 1 lb.) or weaponized oil (1-pint flask) (127, 128) (1 sp; 1 lb.) has a chance of catching on fire its target. (They just deal fire damage.) The Dungeon Master's Guide mentions catching on fire in only two instances: while in a forest fire a creature checks once per minute to see if he catches on fire (88–9), and apparently a creature checks if he catches on fire whenever he's not on fire if unprotected on a plane or in an area of a plane that possesses the elemental and energy trait fire-dominant (148–9). The Monster Manual includes the extraordinary ability burn of the fire elemental and the thoqqua (98 and 242, respectively) but no other ways unwary adventurers can be caught on fire by their monstrous foes.
This dearth of ways to catch on fire inspired me to look elsewhere for ways to do so. So far as I could tell no magic items in the Magic Item Compendium causes a creature to catch on fire. And in the Spell Compendium only the 1st-level Sor/Wiz spell ray of flame [evoc] (SpC 167), the 2nd-level Sor/Wiz spell combust [evoc] (SpC 50), and the 7th-level Sor/Wiz spell elemental body [trans] (SpC 78)—by picking fire, obviously—give casters the ability of cause enemies to catch fire. Even the spell fires of purity in the question was updated from Complete Divine (165) by the Spell Compendium (94) so that the spell no longer causes enemies to catch on fire!
But what if it does come up?
Were catching on fire multiple times to arise in this DM's campaign this DM would have it work as per the question's scenario C. (In fact, this DM is pretty certain that he already ruled that way a while ago when PCs fought some fire elementals.)
Both scenarios A and B, in this DM's opinion, increase far too much the danger involved in catching fire. This DM suspects that a campaign that treats fire like in scenarios A and B will see players Dumpster-diving for every possible way that they can have their PCs catch on fire their enemies… and then use those ways as frequently as possible. With catching on fire as a cumulative dial rather than a static switch, if enemies can be consistently caught on fire, they will be. Thus PCs would need to be equally wary lest they, too, fall victim to fire-using foes who should have long ago discovered fire's incredible efficacy in the campaign.
Ultimately and by extrapolation, this player would certainly participate in a post-Flame Wars campaign in which all the setting's structures are by necessity composed of fireproof materials and the only surviving monsters are those that are immune to fire, but this DM wouldn't want to run that campaign. Thus in my campaigns I'll stick with scenario C, ruling that a creature is either on fire or not on fire instead of ruling that a creature that's already on fire can be even more on firer.
