I read the topic and made a little thinking of my own, and I would like to offer my conclusions to you. Not really a full-thought project, just a draft, but still...
(NB : English is not my first language, so please be kind toward any mistake or unclarity I shall commit...
As Losdia said in the OP, most roles are already covered. Except for maybe unarmed and non-lightsaber melee (some said Teras Kasi, others think of Echani or Mandalorians...) ; some kind of creature/droid handler (but which would need a specific companion-system different from other classes) ; and a primary buff/debuff role - that's the last which inspired my musing.
Yes, it's a more group-oriented gameplay ; but, not necessarily more than a full healer, and since there are companions to accompany the player, that's not completely solo-unfriendly. Moreover, I think adding more classes would target essentially old players, maybe even require some kind of unlock (legacy, or cartel market) ; then classes demanding more skill are not out of the question.
Now, for the mechanic of the class, some people (JacksonMo in this precise topic) stressed the issue of the four primary stat. Well, creating a fifth seems unlikely, but that does not mean we have to choose one of the four existent to our new class.
Let's imagine : at first, since this class would be the most fragile solo-wise, levelling would concentrate mainly on rising endurance. Then, at specialisation, each AC tree's special powers will benefit from a secondary stat, gained from stuff.
As for Advanced Class, I think this could be a class without DPS spec : all classic classes have a DPS spec, and as I said before, this class target more advanced gameplays. So I will be seeing, for instance : as the common tree, passive abilities benefiting self-preservation : personnal shield, evasion tactics, aggro removers, etc. Then, each advanced class would have its own buff/debuff spec tree - one more "buff", the other more "debuff". Finally, one of the spec would have a tank/debuff tree, the other, a heal/buff tree. To continue with my idea of primary stat adapted to specialisation, let's say the tank tree would benefit from strength, the heal tree from willpower , the debuff tree from aim, and the buff tree from cunning.
Now, for the aspect and lore of the class, I think cannot avoid doing, some day or another, the very famous Imperial Guard. The buff/debuff mechanic could be defended story-wise by a strong "band of brother" spirit among the Imperial Guards, and that's a way to differentiate the class from the Republic Soldier.
As for the republic side, I rather agree with Galandro that the Leia/Padme archetype is not really represented by the IA, and a senate/political class would be interessant. The buff/debuff mechanic would be justified by their charismatic point of view, based on democratic principles. I would call thme "nobles" though, as TOR classes all have a the name of a profession ; senate councillor, or some senator's aid, would be better - which does not forbid to mad the story-class rooted in a noble background, just in the same fashion as
Lastly, this doesn't necessary need new beginning planets : for instance, they could just add a zone to capital planets (Coruscant and Dromund Kaas), in the same fashion the added a HL zone to Corellia, and this would be fine story-wise for the classes I depicted...