I could see Classes gaining their own unique skills past a certain level while Jobs branch the other way, but the balancing of that would be a nightmare. Not to mention the inevitable bitching of the community of "WHY CAN'T I USE THAT ABILITY ON MY PLD IT'S UBER ON MY GLA" etc etc.
One thing I can suggest is for classes to use TP more often than the jobs. That's to say, have more abilities that use TP which can THEN be equipped across the classes. Radiance, for example, from the CNJ line of abilities - TP weaponskill, does damage, and regains MP. A good ability even for the melee classes, which allows them a few more precious drops of MP to cure or buff.
What I'm more thinking about is probably best described in a chart...Let's use Conjurer as an example.
Level 1 - Stone [CNJ/WHM]
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Level 2 - Cure [CNJ/WHM]
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....
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Level 30 - Cura [CNJ/WHM]
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(QUEST) Level 30 - Purge [CNJ]------Presence of Mind [WHM]
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Level 34 - Sacred Prism [CNJ/WHM]
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(QUEST) Level 35 - Radiance [CNJ]------Regen [WHM]
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Level 38 - Shroud of Saints [CNJ/WHM]
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(QUEST) Level 40 - Shock Spikes [CNJ]------Esuna [WHM]
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Level 42 - Aerora [CNJ/WHM]
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(QUEST) Level 45 - Boon [CNJ]------Holy [WHM]
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Level 46 - Curaga [CNJ/WHM]
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Level 50 - Repose [CNJ/WHM]
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(QUEST) Level 50 - Coruscation [CNJ]------Benediction [WHM]
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(The following is just speculation on what can be added with level cap raise)
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Level 55 - Reraise [CNJ/WHM]
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(QUEST) Level 55 - Evanescence [CNJ]------Eschaton [WHM]
Explanation of abilities chosen (and my own interpretation):
Purge - removes elemental attributes of target enemy. Meaning that resists against Aero and Stone gets removed, even allowing Fire, Blizzard, Thunder etc. to potentially hit harder given the right circumstances.
Radiance - TP move, deals non-elemental magical damage, chance to regain MP.
Shock Spikes - covers body in electric waves that have a chance at paralyzing the enemy.
Boom - increases cast and recast time to lengthen spell duration of next enhancing spell.
Coruscation - TP move, deals variable non-elemental magical damage, chance to absorb HP and MP. (combo; Radiance - chance to also absorb TP)
Evanescence - TP move, deals high non-elemental magical damage, chance to inflict DoT effect. (combo; Radiance - attack turns into AoE target)
Eschaton - deals heavy holy damage in area of effect around target enemy, chance to inflict Dia effect.
Of course, it's really the system that I'm trying to get through. I feel that the class-quests are a bit of a waste, since they generally don't really do anything for the [Classes] themselves. So they could have class and job quests run parallel, and reward abilities at the end of each questline.
The only condition is that the class abilities gained from questlines can be used by OTHER classes, but cannot be used by jobs. Jobs gain their own specialised abilities.