Vowel modification ("aggiustamento") is the great magic trick / lifesaver of classical singers. There are various theories: always modify towards schwa, always modify towards a more open vowel, etc. and I find that none of these work for me or my students. Their flaw is that they suppose that all vowels need to modify for the same reason.
My theory of vowel modification is this: the real goal is to maintain resonance as a vowel ascends or descends into the extremes of the voice [these, after all, are the only times we modify vowels]. So, the singer must ask, "why is resonance being lost on this vowel?" If resonance is being lost because the vowel is too closed, then we must modify open. If resonance is being lost because the vowel is too open for the extreme range, then we must modify closed.
Now: is the vowel that needs modification a lip vowel or a tongue vowel? If it's a tongue vowel, it will modify towards [e]. If it's a lip vowel, it will modify towards [o]. Yes, it really is that simple!
[NB: In the case of [a], this modifies nicely towards [o], as the famed "Caruso scale" teaches us. The other excellent option when [a] needs modification is [æ]. A little experimentation with a modification to either [o] or [æ] will quickly reveal which works best for a given situation.]
In other words: the [u] of the word "moon" at a high pitch level might lack resonance because of constriction (the natural vowel is too closed to stay resonant). It would benefit from modification towards [o].
On the contrary, the [ʊ] of the word "book" at a high pitch level might lack resonance because the open vowel needs focus (the [ʊ] is too open to stay resonant). It too would benefit from modification towards [o], but for a different reason.
The key is that vowel modification, when it is needed, is needed for different reasons. The written vowel is either too open or too closed to maintain resonance as pitch ascends.
[e] and [o], as the moderate vowels on their respective sides of the vowel chart, have just the right mixture: they have adequate space to feel comfortable singing as pitch ascends, but adequate closure to easily resonate on both very high and very low notes.