Only having four classes was always a downside for TESO, one that I think turned a lot of people off from the game. Having played MMORPGs off and on for about 12 years, I believe that this suggestion could vastly increase replayability and draw in more people from other MMOs, especially those who heard that the options for classes were so few and so restrictive.
So here is my suggestion, Advanced Classes or "Dual Classing".
To unlock Advanced Classes you must first level two characters of different classes to level 50. This allows you to change either of their Base Classes to an Advanced Class, using Skill Lines from each one. Two Advanced Classes exist between each of the Base Classes, and both are unlocked at the same time. For example, if you leveled a Nightblade and a Sorcerer to 50, you can make either or both of those characters into Ritualists or Demonologists.
If you have a level 50 Templar, Sorcerer, Nightblade AND Dragon Knight, your characters can become any Advanced Class connected to their original class, potentially 6 total Advanced Classes per character. For example, your level 50 Templar could become a (Dragon Knight) Warden, Zealot, (Sorcerer) Evoker, Apostate, (Nightblade) Heretic or Seer.
Each Advanced Class, like existing classes, can have only 3 Class Skill Lines. Two of the Skill Lines are chosen for you depending on the Advanced Class you pick, the third is entirely up to you and may be reassigned later for a Scroll of Knowledge (50 Pack = 50 Crowns). Advanced Classes may be abandoned for 50 Crowns, returning you to your original class and allowing you to choose a new one or remain as a Base Class.
The image is pretty self-explanatory, some of the names and given Skill Lines may need tuning, but this is essentially what I think could help the game.
Sorcerer/Nightblade - Ritualist & Demonologist
Nightblade/Templar - Heretic & Seer
Templar/Dragon Knight - Warden & Zealot
Dragon Knight/Sorcerer - Shaman & Occultist
Dragonknight/Nightblade - Reaver & Shadowflame
Sorcerer/Templar - Evoker & Apostate
Personally? (And clearly I am biased.) I would be infinitely more excited to play my Sorcerer as a Shaman with Earthen Heart, Ritualist with Siphoning or Evoker with Restoring Light.