Could have, if they were great and enlightened before becoming Greater Akuma maybe.
But by default a Greater Akuma gets access to Level 7 Disciplines and is generally treated as if that were his Dharma-level for most matters.
Exept perfect control over his shadow-soul and a bigger pool of Chi, I think.
They get access to 7 dot traits as a base line max and then can bust that limit with Soul Treatments and lesser Investments.
Say that we face someone whose had the:
Graceful Reed Angel treatment for extra four dots of Yin and Yang Prana, so has Yin Prana 10 and an extra Yin Prana 8 power, as well as having four bonus dots to each of Dexterity and Martial Arts, to make them 10 (or eleven of that's possible).
As well as;
Beatifically Enlightened Tutor Treatment, giving four extra dots to perception, six extra dots to rituals, and two dots to Internalise giving them Internalise 9 and Chi'uh Muh 9. You then apply the Unfolding Scarlet Lotus Investment to push them both to 10.
As mentioned above, you then add on a whole pile of lesser investments of the Unfolding Scarlet Lotus which gives you an extra cap-breaking dot in a discipline. A greater akuma is likely to have been an extraordinary enough character that they could have this applied to quite a few additional disciplines to push them up to level 8.
As a result, when rebuilding a greater shikome Emma-O could easily give them three ten dot disciplines.
If he wanted to be more optimised, he might be able to go with Saint of the Godbody and Beatifically Enlightened Tutor Treatment plus Unfolding Scarlet Lotus to raise four of the Shintai plus Internalise and Chi'uh Muh to ten dots, although that may be challenging because of Attribute prerequisites needing lots of Iron Hand investments.
Basically, a Greater Akuma can be relied on to have 10 on any attribute or ability particularly relevant to their job and rank ten in three to six disciplines.
Greater akuma are rare and they're the kind of thing you want a circle of experienced celestials or multiple war-wu of ancient vampires to face.