I suppose if they were to do it (which wouldnt be completely game breaking, but must take into consideration how armor/gear is afflicted by it), the following things SHOULD be manageable without too much alteration to the current engine:

1) More Face options - Not just faces themselves, but variable components of the face too. Doubling what they have would go a long way in helping promote a different look.
2) Broader height ranges - Height sliders should be a bit broader. As it is now, with some races, the height slider does not actually give you that much difference.
3) Muscularity sliders - All races should have this (including Lalafells)
4) Unlocked attributes that dont make sense locked - This is more specific to AuRa and their horns. You should be able to choose horns independently of Face
5) Colorization of certain aspects - Again, more towards Aura, but Scales should have a color range you can choose from. The current Blue-Black, and Off-White color palettes actually limit what skin tones you can use, due to certain skins looking horrendous with those colors.
6) (A controversial one) Actually make the "chest" slider for Lalafells represent something or remove it outright - Ive mentioned in other threads that Im not 100% a fan of some of the aesthetics of Lalas in general, but there are issues with the design of the race that should be addressed. The Chest slider, for whatever purpose, exists on female lala but has no actual 'impact on their appearance. I can speculate that the reason has to do with the idea that they dont want to get hit with 'sexualization' issues. However, since we all know thats a half measure considering the glamour and emotes possible in game as it is, its kind of a moot point. Furthermore, Lala's by design have very little distinction between males and females. While I get that theres more to girls than chest assets, it is a very easy short hand to differentiate between men and women, and also may help bust some preconceived notions about Lalas being too "kid like". Should they not adjust it, they should remove it in favor of other sliders to help differentiation between the sexes or an extra customization option for Lalas in general. Either/or is fine, but they need to either own the slider or remove, and not have some vestigial customization that amounts to nothing.
7) Scars and other minor aspects - All races have access to All Scars and/or any other aspects (beauty marks as an example). Scars should be available not only for Face, but also Body.
8) Facial tattoos - You should be able to select multiple at the same time.

Things to be changed outside of character editor:

These are facets that can help with customization but dont require implementation to the character editor itself. Basically, they should be aquired VIA MGP at GoldSaucer or through POTD/HoH or Achievements

1) Unlock glamour that alters between races - Things like the hempen camise as an immediate example should be available to all races. The 'start' race should either receive it through a quest or by default, but should be able to aquire the other ones
2) Unlock Emotes based on Race - Any major emote variation based on race should be acquirable.
3) Unlock Hairstyles - Any hairstyles that are race specific should be free for the start race you have, but the others have to be unlocked
4) Eye Colors and Hair Colors - New eye and hair colors should be acquired via GS
5) New tattoos should be acquired via Gold Saucer
6) Body Tattoos - Tattoo Artist Unlocked Via GS, with a base set available and additional Tattoos unlocked via MGP or other sources
7) Piercings - Body and Face piercings could be unlocked along with Tattoos and additional ones acquired via MGP or other sources

I think these kind of changes, while not the exacts of everyone here, would be broadly accepted as a decent step and be well received without making huge alterations to the engine itself.