I have been positing a version of this
before, but now put in the effort to rework it a little after the appearance of the Warden class... updating the concept which I still think would be pretty nifty for ESO (but then I would, wouldn't I?)
Anyways, here it goes (please don't hurt me

):
Personally I would think the best way to add more "classes" is to give each class, say, three different "class morphs", each with its own new skill/passives line. Perhaps becoming available after completing the main storyline… or possibly only after doing cadwells silver... to reward people who do play through that – which would also give people the whole of cadwells gold to focus on making this new skill line since in my experience that was the point where I had maxed all my basic class and guild skills on most of my characters… (a "reward" for finishing cadwells gold might be some alliance change quest, but that is another topic, to be discussed elsewhere…)
The basic idea is that you may get to "morph" your basic class into an advanced version, gaining an fourth skill tree in addition to the basic three, with three different "morph flavor" choices per basic class; such a morph could of course be redone just like skill morphs (though as with them, any new choices would need their skills maxed from the beginning)
These morphs could become simply available to choose at completion of some checkpoint quest (like mentioned, cadwells silver would be one possibility, the mainstory another for those people who really don’t like to quest a lot), though it might also come as part of some quest…
I think it actually would be great if one had to follow a "find the right trainer" quest to morph ones basic class to any of those advanced classes, which might make a nifty addition to ESO, could be a whole small guild-sized DLC... not even needing its own fullsize region, it could be a DLC that adds several locations all over the place to go and search for that master… a hidden nightblade training facility in some lonely alik’r mountain fortress; a secluded sorcery school in an separate oblivion plane, a templar cathedral to the divines standing proud at the cyrodil border, a dragonknight practice arena run by descendants of the imperial akaviri (perhaps even in an instanced cloud ruler temple!), a warden gathering place in the heart of skyrim woodlands... something like those ideas anyhow.
It might also be possible to do this as a package deal. Like… have one questline dependent on each basic class, and choices with diverting paths, and depending on how your character goes through the questing might determine your available class morph… also possibly with factions, side with this one, gain this morph at the end of the questline, side with that one, gain that morph… et cetera.
It might be too much to ask, but it definitely would be more interesting if this concept came with some questing to unlock new options (though I suppose hardcore PvPlayers might hate it – but then ZOS could always sell insta-class-morphin tokens in the crown store, just like for vampire or werewolf...)
Some possibilities:
Dragonknight
Gladiator (offensive self buffs & warcries; color: red/orange)
Pyromancer (flame resist and even more fire; color: yellow/blue - gas flame!)
Warlord (defensive group buffs, AoE standards, color: purple/gold)
Nightblade
Illusionist (illusion summoning, mind magic; color: red/black - NPC illusionist)
Monk (melee support & assorted “martial arts” magic; color: blue/purple)
Scout (stealth support and defense buffs; color: olive-khaki)
Sorceror
Necromancer (death magic and undead summoning; color: cyan - NPC coldfire)
Spellsword (melee support & buff magic; color: yellow/orange – golden lightning!)
Warlock (arcane magic; color: purple-ish, like NPC warlocks)
Templar
Crusader (melee support and aura-style buff magic; color: white/gold – holy light)
Pilgrim (buff magic and healing support; color: yellow/green)
Witch-hunter (counterspells, spell resistance/shields, silencing; color: purple/red)
Warden
Cryomancer (ice magic, color: white/clear - NPC cryomancer)
Ranger (animal summoning and nature magic; color: brown/green)
Shaman (nature magic, totems, summons; color: shades of green)
Another possible idea was to not only have an added skill line with its own flavor of visual effects, but maybe even morph the existing effects to match.
So for example if a sorceror goes necromancer, their spells might be color-shifted to necromancer "coldfire" cyan, and if they turn warlock, their lightning may turn purple instead of white-blue, or a nightblade going scout would have their reddish effects recolored to something camo-ish olive green & khaki brown... that sort of stuff. For more visual goodieness and varietee between classes.
Perhaps even morph the spell effects to some degree... like, for summoned armor might look daedric on normal sorc, something magic-ish arcane on warlock, worm cult / lich on necromancer, and some knightly style on spellsword, etc.
That idea might perhaps take a bit too much coding to be viable though... I'd be happy with pure color shifts.
...of course, all those quick ideas are just very rough concepts, without much consideration but character fluff. I merely tried to give some options, and went for three instead of just two "magica-specialization / stamina specialization" - It's supposed to be more for added character diversity then anything else after all. And I had to rework them from the first version with the introduction of the warden, shift some ideas, add more to compensate…
Thus for example with Nightblades, there might be one magica-caster based with "illusionist"; one stamina melee based with "monk" (Yes, a nod at the old D&D class of the name, the first “martial arts” powered class I remember in fantasy gaming); and finally I went for "scout" as sneaky survivalist option after shifting the animal-flavored idea to warden…
Similar thoughts for the Sorceror - "spellsword" for stamina sorcerors; replacing the original cryomancer idea I came up with "warlock" as standoff caster class and to grab those "Witch/Warlock NPC" abilities I always wanted for player characters as well; and "necromancer" because all too many people really, really want that...

Templar... has "crusader" is for stamina templars as the class name has been appearing in TES games before, despite tamrielic religions having less a focus on "cross" then where the name originated, and my "witch-hunter" idea is kinda inspired by the spanish inquisition (Yes, I know noone expected that

), its "warhammer" imperial counterpart and also "Dragon Age", I admit it... seems logical to set up the aedric-flavored templars as natural enemies of the more deadric-flavored sorcerors... and finally replacing the warden-gone shaman idea came a "pilgrim" as support and summoner class...
Dragonknight I had the fewest ideas, since I kinda dislike that class. More fire magic for dragonknight magica-casters with "pyromancer" is a natural first thought... so then I went with "warlord" as "leader-style group play support" and "gladiator" as "berserker-style single combatant" flavors, though there may be better ideas then those...
Finally, for the new Wardens I grabbed some of my original ideas from other classes as they fit better, the "shaman" is a very natural idea, between all those druid-type characters like breton wyressess, argonian treeminders and bosmer spinners, expanding on the wardens plant-healing nature magic with some more aggressive plant based spells was rather obvious; "cryomancer" since ice staves have no matching offensive skill line yet (while fire and lightning staves sort of have) while the warden ice skills are generally more tanky in nature; and "ranger" was also pretty obvious, and giving them even more woodland creatures to call as well as some related skills for the "hunter" playstyle would seem applicable.
The skills itself are also just rough concepts - some I am quite happy with, others I feel might benefit from more thought and ideas… but it's a start I suppose, a proof of concept kind of notion, something like that… with ample room for refinement and reworking.
(also note that many of those I "borrowed" from existing mobs without knowing the actual in-game name of the abilities, just by remembering what I could from the time some mob used them unsuccessfully against one of my characters, so please, don't get too hung up on the names I used here, all right?

)
In any case, since more diversity is always something I would love to see... much more fun having more choices in realizing your "perfect" character, especially since the limited number of skills one can actually use at any one time (5+U) makes people having to think and choose anyhow, so adding more active skills only increases a characters choices, not exactly their power...
And yes, spellcrafting might be able to cover some of those... but for one spellcrafting won't give you passives, which these skill lines should, and for another we have no idea whatsoever if, when or how spellcrafting might ever come to ESO... so I would rather put out an good (hey, at least I think so

) idea then bet on a far off "maybe"...