Well, if the question of the transcendentals' relation to each other is supposed to be a priori, having nothing to do with how things are arranged in nature, their unity or disunity would be trivial, stipulative, and game-like, a matter of defining terms. Plato can say there's a faculty of rational intuition that accesses the Forms, but that's just an elitist rationalization.

Judging from the empirical evidence, the three transcendentals aren't united. Socrates' physical ugliness led Plato to talk about inner kinds of beauty, and the like. But it's much simpler to argue that we should expect a righteous truth-seeker like Socrates to have been less than beautiful or handsome since the latter quality conflicts with the other virtues.

Outward beauty is liable to corrupt the character, given beauty's social utility. And philosophical and moral inclinations are likely to count against inner beauty or harmony of character, too, since truth and idealism are alienating in the real world (the latter being run on happiness-sustaining delusions).