I'm also curious about possible additional aspects of personality that aren't included in these sub-traits. Are there other tests or theories that consider different attributes of personality?
It's important to note that FFM works from Traits, meaning measurable tangible effects via answers.
The factors that are listed are what they view as the main grouping of personality differences. Outside this groupings there are very few that are consistent (meaning less personality and more specific behavioral stuff, like disorders).
Effectively, what they did is ask a boatload of questions, did factor analysis to find the main groupings (the main five) which were a bunch of data points that were linked together - for the most part.
Meaning that one tends to have multiple + or - parts within the main trait. Of course, this variation is quite large in an individual (or can be, if you prefer).
Is there more to it? Yes. But in terms of measuring someone, you will overload if you step it up another level (which is not about adding just one or two traits, but a whole slew of them, all of which don't tend to apply to everyone... very difficult to measure that and in general specific tools measure them. This is getting out of my area of expertise, but I believe that is the jist of it).
Nightning, have you taken the NEO-PII? Has anyone here taken it? How would I go about taking it?
Edit: That's the gold standard for measuring the Big 5 including all facets of sub-traits.
You can find a... how do you say... short form test of just NEO
here. It also has a scoring guide. No breakdown of note, however...
Far as I know the NEO-PII is controlled and has to be administered by a professional.
(I say this as I'm hunting for someone to administer KAIT, and it's very frustrating.)