Good input all around. The Cross Class Combos wouldn't just be limited to damage - that was just for the sake of the example. There are other things that could be added for capitalizing on one of the status effects. In addition to +Damage things like:

Life Leech
Mana Leech
DoT
Stun
TP Wipe
Anything else players/devs think of

Personally, I like where this is going. I with DarkOrca. An idea like this should completely replace BR. To Crowley, the OP mentioned that the status effect would be applied by the class, not the skill, so that covers the "requires: X", but your concern is valid in the case that the status effect lasts long enough for a player to go through the motions of swapping class and rebuilding TP in the heat of battle.

The one thing I would suggest is making the skills only able to benefit from one other status effect, two at most. Otherwise they have a bit too much utility. Well, that's my opinion, at least.
Yes, thank you for the clarification on how the effects are applied. The duration would only be a few seconds long. Nowhere near long enough to switch class mid-battle! Good thinking though. In the example I gave the LNC skill could chain off 4 effects. 2 for +75% and 2 for +50% damage. That too many?

1. Scrap the current BR system but instead bring back the a more elaborated SC system from FFXI - to my understand, Kashius's idea is basically very similar to how SC works but with many more combinations. Players can chain different skills after one another for bonus effect
The main difference is that you don't have to chain skills. You chain off the effect. Each class would have several different ways to inflict the status on an opponent. For instance, ARC in the example have several options (Puncture (WS), Passive, Raging Strike). Perhaps GLA would be able to inflict their status off blocks (% chance based on the block. 100% for full block and another % for partial). THM could have a chance for their effect to be triggered from each tick of a DoT.

I'm attempting to set up a system that allows for opportunities to randomly do some extra damage in a PUG or really lay into a mob with a coordinated routines.

2. Add a system where players can "combine" two skills together (instead of chaining them). These combined move can be setup prior to battles to make things easy. For example, two players in a pt can setup a "fire + puncture", which can be activate when both players have the required tp/mana/timers. When one of the player triggers it, both players will do the corresponding move (ie: Arc doing puncture and mage casting fire onto the Arc or whatever ;P) for the combined effect.
I've always thought that mages should have an activated ability that allows them to target an ally with a spell to buff that ally with bonus damage of that type for a set time/next attack. I would have to be balanced so that there is an actual bonus. If the bonus damage is only 50 and the mage can solo cast the nuke for 70 no one would do it. But I do like the idea and I wish they would implement it in a way similar to the opening movie!

Keep those wheels turning!